HARMONY  IN 
PI  ANOFORTE-  STUDY 


liflilHltnil 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 
Benno     Rubinyi 


HARMONY  IN 
PIANOFORTE-STUDY 


HARMONY  IN 
PIANOFORTE-STUDY 


A  BOOK  FOR  THE  INDIVIDUAL  STUDENT 
BY 

ERNEST   FOWLES 

FELLOW  OF  THE  ROYAL  ACADEMY  OF  Music; 
AUTHOR  OF  "STUDIES  IN  MUSICAL  GRACES,"  ETC. 


G.  SCHIRMER,  INC.,  NEW  YORK 

British  Publishers:  J.  CURWEN  &  SONS  (LTD.),  LONDON,  W. 


COPYRIGHT,  1918,  BY 
G.  SCHIRMER,  INC. 

28036 


Printed  in  the  U.  S.  A. 


Music  Libnn 

MT 


TO  MRS.  CURWEN 

IN   GRATEFUL  ACKNOWLEDGMENT  OF 

A  HELPFUL  FRIENDSHIP  OF 

MANY   YEARS 


THE  AUTHOR'S  APOLOGY 


THE  following  pages  contain  a  digest  of  principles  formulated 
by  the  writer  for  the  use  of  his  pianoforte  students.  In  com- 
mon with  his  colleagues  generally,  he  has  continually  to  deal  with 
those  whose  harmonic  knowledge  and  perception  are  of  the  slightest; 
and  who,  moreover,  are  unlikely  to  acquire  more  than  may  be  af- 
forded to  them  in  the  course  of  instrumental  study.  The  book  is 
not  intended  to  supplant  the  work  of  the  expert  teacher  of  harmony; 
more  exactly,  it  may  be  regarded  as  a  means  of  feeling  the  harmonic 
pulse  of  the  student  at  the  weekly  instrumental  lesson.  It  presents 
the  subject  in  the  most  elementary  manner.  It  professes  to  appeal 
both  to  the  harmonist,  strong  in  a  grasp  of  part-writing,  and  to  the 
student  whose  mind  is  innocent  of  such  attainment.  To  the  one, 
it  may  be  a  help  to  bring  his  theory  into  touch  with  the  living  or- 
ganisms of  actual  music;  to  the  other,  it  may  prove  a  bracing  me- 
dium, stimulating  him  to  the  inquiry  why  these  things  should  be. 
More  than  this,  indeed,  is  not  attempted;  yet  it  may  be  confidently 
asserted  that  the  pianoforte  teacher  who  will  yield  five  minutes  of 
the  time  of  each  lesson  to  the  type  of  study  here  outlined  will  reap 
a  considerable  reward  in  the  increasing  perception  of  the  use,  nature, 
and  purpose  of  harmony,  on  the  part  of  his  students. 

It  is  given  to  all  with  average  intelligence  to  write  a  chordal  pro- 
gression in  accordance  with  every  rule  devised  by  the  wit  of  harmon- 
ists; it  is  given  to  those  only  who  have  received  a  measure  of  musical 
illumination,  spontaneously  to  play  such  a  progression  with  entire 
acceptance  to  the  musical  sense.  The  latter  achievement  is  the 
higher;  and  when  the  student  has  reached  the  power  so  to  link 
chords  with  unpremeditated  and  yet  with  aesthetic  charm,  he  has 
crossed  the  Rubicon  of  all  harmonic  endeavour. 

24,  BERNERS  STREET, 
LONDON,  W.  i. 


vii 


TO  THOSE  ABOUT  TO  USE 
THIS  BOOK 

A  LARGE  part  of  the  effect  of  music  is  concerned  with  harmony: 
since  this  is  so,  it  behooves  every  music-lover,  listener  as  well 
as  player,  to  cultivate  the  sense  which  recognizes  the  harmonic 
basis  upon  which  virtually  every  musical  progression  is  founded. 

The  mental  necessities  which  underlie  the  study  of  harmony 
include:  —  (i)  A  knowledge  of  the  properties  of  chords  and  of  the 
sounds  generally  by  which  they  are  accompanied.  (2)  A  keen  aural 
grasp  of  any  possible  combination  of  sounds  that  may  be  used  in 
music.  (3)  The  power  to  conceive  harmonic  progressions  unaided 
by  any  other  medium  than  that  afforded  by  the  trained  inward  sense. 
(4)  The  ability  spontaneously  to  express  these  combinations  and 
progressions  at  the  keyboard.  (5)  The  facility  to  express  the  same 
combinations  and  progressions  upon  paper. 

The  older  methods  of  teaching  the  subject  —  now  rightly  dis- 
credited—  laid  undue  emphasis  upon  (i)  and  (5).  A  perception 
of  the  importance  of  (2)  prepared  the  way  for  a  recognition  of  the 
claims  of  (3),  and  contributed  indirectly  to  the  great  advance  in 
the  expression  of  harmonic  thought  upon  paper  which  followed  the 
adoption  of  sane  aural  methods.  But  however  thorough  may  be 
the  method  of  (5),  it  is  too  cumbrous,  too  lacking  in  spontaneity  to 
respond  immediately  to  the  conceptions  of  the  inward  sense.  It  is 
for  this  reason  that  (4)  assumes  a  role  of  infinite  importance  in 
dealing  with  what  may  be  termed  the  synthetic  aspect  of  harmony. 
•  It  is  the  tendency  of  those  whose  harmonic  discipline  has  been 
confined  to  paper  work  to  regard  the  chord  solely  from  that  par- 
ticular aspect  so  aptly  described  by  the  French  expression,  harmonie 
plaquSe.  The  tritest  of  examinations  will  prove  that  the  presen- 
tation of  harmony  in  this  form  is  comparatively  rare  in  instrumental 
music,  which  inherently  demands  a  large  share  of  that  phase  of  har- 
monic expression  known  as  harmonie  figuree.  Yet  both  types  may 
frequently  be  observed  within  the  same  work.  The  first  movement 


Vlll 


To  Those  About  to   Use  This  Book  ix 

of  Beethoven's  Sonata,  Op.  53,  contains  examples  of  harmonic  plaquee 
(bar  35  et  seq.)  and  of  harmonic  figuree  (bar  50  et  seq.) ;  but  the  great 
mass  of  the  movement  is  concerned  with  the  latter  rather  than  with 
the  former.  Such  being  the  case,  it  is  evident  that  the  student 
should  endeavour  strenuously  to  cultivate  the  power  of  presenting 
harmony  in  the  florid  manner  advocated  in  this  book. 

The  fundamental  and  indispensable  condition  of  success  lies  in 
the  conquest  of  Part  I.  The  student  who  has  wholly  mastered  this 
Part,  who  is  able,  in  an  interesting  manner,  to  present  the  harmonic 
progressions  it  unfolds,  is  not  likely  to  encounter  any  serious  barrier 
to  the  mental  grasp  of  the  principles  enunciated  in  the  remaining 
Parts.  The  power  to  present  harmonies  in  simply-embellished  form 
and  without  the  help  contributed  by  the  use  of  auxiliary  sounds, 
a  virtual  making  of  bricks  without  straw,  is  a  preparation  indis- 
pensable to  the  ultimate  expression  of  musical  thought  in  free  ex- 
temporaneous form. 

Although  the  order  assigned  to  the  various  Steps  is  the  outcome  of 
the  author's  own  experience  in  the  training  of  students,  he  would  be 
the  first  to  concede  that  this  order  may,  and  indeed  should,  be  varied 
in  accordance  with  the  needs  of  the  individual.  Thus,  for  a  certain 
type  of  student,  the  following  schedule  may  at  first  be  found  neces- 
sary:—Steps  I,  II,  VII,  VIII,  XIII,  XV,  XVII,  XVIII,  XIX,  etc., 
the  intervening  Steps  being  negotiated  after  these  have  been  mas- 
tered. 

The  only  objection  that  can  be  urged  against  the  course  of  study 
advocated  here  is  that  it  does  not  make  for  progress  in  the  art  of 
part-writing.  This  is  by  no  means  the  evil  that  some  may  think  to 
be  the  case.  Counterpoint  is  the  medium  par  excellence  for  acquiring 
facility  in  part-writing;  harmony  is  the  medium  whereby  the  stu- 
dent learns  to  manage  the  masses  of  combined  sounds  in  the  form  of 
chords  unknown  to  the  science  of  strict  counterpoint.  The  part- 
writing  of  the  harmonist  depends  upon  the  power  he  has  acquired 
in  this  respect  from  contrapuntal  study.  The  niceties  of  part- 
management  in  writing  for  voices  have  little  to  do  with  the  handling 
of  chords  intended  solely  for  keyboard  expression.  If  it  be  disal- 
lowed to  thrust  the  specialities  of  harmony  upon  counterpoint,  then 
the  converse  must  also  be  true  —  that  the  rigours  of  counterpoint 
should  not  be  permitted  to  usurp  the  purely  and  primarily  harmonic 
function. 

In  those  cases  where  ignorance  of  the  fundamental  principles  of 


x  To  Those  About  to  Use  This  Book 

harmony  is  an  unavoidable  condition,  the  teacher  of  resource  will 
refrain  from  perplexing  the  student  with  a  copybook  review  of  rules 
which,  however  indispensable  to  the  study  of  harmony  in  well-par- 
ticularized parts,  are  often  a  deterrent  to  the  successful  portrayal 
of  harmonic  shapes  upon  the  pianoforte  keyboard.  The  latter  ac- 
quirement depends  upon  the  capacity  to  perceive  what  is  or  is  not 
radically  musical.  When  a  student  contrives  to  present  two  chords 
with  consecutive  octaves  between  the  extreme  sounds,  or  if  perchance 
he  alight,  let  us  say,  upon  consecutive  fifths  under  like  conditions, 
it  is  easy  to  point  out  that,  in  the  one  case,  he  offends  upon  the  ground 
of  monotony,  and,  in  the  other,  that  his  crime  is  against  the  law  of 
expediency.  More  than  this  in  the  way  of  precept  it  is  unnecessary 
to  attempt;  less  than  this  would  negative  every  impetus  towards 
real  advance. 

The  insistence  upon  self-expression  in  the  major  and  minor  modes 
alternately  is  a  particular  feature  of  this  book.  It  will  be  observed 
that  illustration  is,  in  every  case,  directed  to  the  minor  of  the  same 
tonic  as  the  foregoing  major  key,  this  being  —  in  the  author's  opin- 
ion —  the  most  natural  way  to  emphasize  the  tonal  contrasts.  It  is 
open  to  the  teacher,  however,  to  use  the  minor  key  of  the  same 
signature  if  he  find  it  more  convenient  so  to  do. 

It  will  be  natural  to  many  a  student  to  be  affrighted  at  the  ex- 
tensive number  of  "Steps"  provided  for  his  delectation.  He  may, 
however,  be  reassured.  In  many  cases,  it  will  be  possible  to  take 
a  number  of  Steps  simultaneously;  in  other  instances,  the  fact  that, 
at  first,  one  only  is  advisable  at  a  time,  will  go  far  to  prove  the  ur- 
gency of  this  type  of  work,  and  will,  at  the  same  time,  act  as  an  in- 
centive to  keen  and  ever  keener  studentship.  Moreover,  it  is  not 
the  number  of  Steps  mastered  which  will  ultimately  count,  so  much 
as  the  accumulative  influence  of  daily  effort  and  the  consequent  de- 
velopment of  the  faculty  to  think  harmonically  as  well  as  melodi- 
cally. 

It  is  almost  futile  to  add  that  a  preliminary  aural  grasp  of  every 
harmony  presented  upon  the  keyboard  should  be  the  consistent  aim 
throughout,  so  obvious  is  the  fact;  yet,  the  student  who  desires  to 
obtain  every  advantage  from  the  study  of  the  following  pages  will 
do  well  continuously  and  courageously  to  keep  this  fact  before  his 
mind.  Only  in  this  way  is  it  possible  to  conceive  that  real  and  per- 
manent power  will  at  length  become  his  assured  possession. 


CONTENTS 

PAGE 

DEDICATION v 

THE  AUTHOR'S  APOLOGY .'. . .  vii 

TO  THOSE  ABOUT  TO  USE  THIS  BOOK viii 

INDEX  TO  THE  STEPS xii 

THE  PARTS: 

I.     PLAIN  HARMONY i 

II.    AUXILIARY  SOUNDS 33 

III.  CADENCES 49 

IV.  CHORDAL  TRANSFERENCE 58 

V.    SEQUENCES  AND  PEDALS 66 

VI.     CHROMATIC  HARMONY 72 

VII.    THE  BUILDING  OF  THE  DOMINANT  DISCORD 80 

VIII.    THE  ENHARMONIC  PRINCIPLE 83 

THE  AUTHOR'S  FINAL  NOTE.  87 


INDEX  TO  THE  STEPS 


STEP 


SUBSTANCE 


PACK 


I.    Major  common  chords  in  root- position I 

II.   The  decoration  of  the  same       2 

III.  First  inversions  of  major  common  chords 4 

IV.  The  decoration  of  the  same 5 

V.    Second  inversions  of  major  common  chords 5 

VI.   The  decoration  of  the  same 6 

VII.    Minor  common  chords  in  root-position 6 

VIII.   The  decoration  of  the  same 6 

IX.   First  inversions  of  minor  common  chords 6 

X.   The  decoration  of  the  same 6 

XI.    Second  inversions  of  minor  common  chords 6 

XII.   The  decoration  of  the  same 6 

XIII.  The  appreciation  of  the  dominant  harmony  in  the  major  key     .  7 

XIV.  The  dominant  and  tonic  harmonies  contrasted      7 

XV.   The  succession  of  the  dominant  and  tonic  harmonies  in  the 

major  key 7 

XVI.   The  decoration  of  the  same 8 

XVII.   The  intensive  treatment  of  the  chords  of  Step  XV 10 

XVIII.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XV . .-••-. II 

XIX.   The  appreciation  of  the  dominant  harmony  in  the  minor  key    .  n 
XX.   The  succession  of  the  dominant  and  tonic  harmonies  in  the 

minor  key 12 

XXI.   The  decoration  of  the  same 12 

XXII.   The  intensive  treatment  of  the  chords  of  Step  XX 12 

XXIII.  The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XX 12 

XXIV.  The  appreciation  of  the  subdominant  harmony  in  the  major 

key 13 

XXV.   The  succession  of  the  subdominant  and  tonic  harmonies  in  the 

major  key 13 

XXVI.   The  decoration  of  the  same 13 

XXVII.    The  intensive  treatment  of  the  chords  of  Step  XXV 13 

XXVIII.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XXV 14 

XXIX.   The  appreciation  of  the  subdominant  harmony  in  the  minor  key  14 
XXX.   The  succession  of  the  subdominant  and  tonic  harmonies  in  the 

minor  key 14 

XXXI.   The  decoration  of  the  same       14 

XXXII.   The  intensive  treatment  of  the  chords  of  Step  XXX 15 

XXXIII.  The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XXX        15 

XXXIV.  The  succession  of  the  subdominant,  dominant  and  tonic  har- 

monies in  the  major  key 15 

XXXV.   The  decoration  of  the  same 16 

XXXVI.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XXXIV 17 

xii 


Index  to  the  Steps 


Kill 


STEP 


SUBSTANCE 


PAGE 


XXXVII.   The  succession  of  the  subdominant,  dominant  and  tonic  har- 
monies in  the  minor  key 17 

XXXVIII.   The  decoration  of  the  same       " 17 

XXXIX.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XXXVII      17 

XL.   The  appreciation  of  the  supertonic  harmony  in  the  major  key  .      18 
XLI.   The  succession  of  the  supertonic,   dominant  and  tonic  har- 
monies in  the  major  key 18 

XLI  I.   The  improvisation  of  melodies,  closing  with  the  progression  of     19 

Step  XLI 

XLIII.   The  appreciation  of  the  submediant  harmony  in  the  major  key      19 
XLIV.   The  succession  of  the  submediant,  dominant  and  tonic  har- 
monies in  the  major  key 19 

XLV.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XLIV 20 

XLVI.   The  appreciation  of  the  mediant  harmony  in  the  major  key  .    .     20 
XLVII.   The  succession  of  the  mediant,  dominant  and  tonic  harmonies 

in  the  major  key      21 

XLVI  1 1.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  XLVII      21 

XLIX.   The  appreciation  of  the  chord  of  the  dominant  7th  and  its  in- 
versions       21 

L.   The  resolution  of  the  chord  of  the  dominant  7th  in  the  root- 
position     ...     22 

LI.   The  resolution  of  the  first  inversion  of  the  dominant  7th    ...     22 
LI  I.   The  resolution  of  the  second  inversion  of  the  dominant  7th   .    .     23 
LI  1 1.   The  resolution  of  the  third  inversion  of  the  dominant  7th  ...     23 
LIV.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  L 24 

LV.   The  succession  of  the  chords  of  the  supertonic,  dominant  7th  and 

tonic  in  the  major  key 24 

LVI.   The  same  with  the  chords  in  inverted  form 25 

LVII.   The  improvisation  of  melodies  closing  with  the  progressions  of 

Steps  LV  and  LVI 25 

LVI  1 1.   The  succession  of  the  chords  of  the  submediant,  dominant  7th 

and  tonic  in  the  major  key        25 

LIX.   The  same  with  the  chords  in  inverted  form 25 

LX.   The  improvisation  of  melodies  closing  with  the  progressions  of 

Steps  LVIII  and  LIX 25 

LXI.   The  succession  of  the  chords  of  the  subdominant,  dominant  7th 

and  tonic  in  the  minor  key 26 

LXII.   The  succession  of  the  chords  of  the  submediant,  dominant  7th 

and  tonic  in  the  minor  key        26 

LXI  1 1.   The  improvisation  of  melodies  closing  with  the  progressions  of 

Steps  LXI  and  LXII 27 

LXIV.   The  appreciation  of  the  supertonic  harmony  formed  upon  the 

ascending  melodic  minor  scale       27 

LXV.   The  appreciation  of  the  supertonic  harmony  formed  upon  the 

harmonic  minor  scale      27 

LXVI.   The  succession  of  the  supertonic,  dominant  and   tonic  har- 
monies in  the  minor  key 28 

LXVII.   The  improvisation  of  melodies  closing  with  the  progression  of 

Step  LXVI 28 

LXVI II.   The  appreciation  of  the  mediant  harmony  formed  upon  the 

descending  melodic  minor  scale 28 

LXIX.   The  appreciation  of  the  mediant  harmony  formed  upon  the  har- 
monic minor  scale 29 

LXX.   Tonal  environment  in  respect  to  major  common  chords      ...     30 


XIV 


Index  to  the  Steps 


STEP 


SUBSTANCE 


PAGE 


LXXI.    The  same  in  respect  to  minor  common  chords       31 

LXXII.   The  improvisation  of  progressions  exemplifying  the  less  usual 

resolutions  of  the  chord  of  the  dominant  7th 32 

LXXI  1 1.   Combinations  of  the  chords  treated  hitherto 32 

LXXIV.   The  elementary  appreciation  of  auxiliary  sounds 34 

LXXV.    Diatonic  auxiliary  sounds  applied  to  the  single  sounds  of  major 

common  chords 34 

LXXVI.   The  same  inverted 35 

LXXVII.   The  same  applied  to  the  single  sounds  of  minor  common  chords  35 
LXXVIII.    Chromatic  auxiliary  sounds  applied  to  the  single  sounds  of 

major  common  chords 35 

LXXIX.    The  same  inverted 35 

LXXX.   The  same  applied  to  the  single  sounds  of  minor  common  chords  36 
LXXXI.    Diatonic  auxiliary  sounds  exemplified  by  scale-passages  formed 

upon  major  common  chords 36 

LXXXI  I.   The  same  applied  to  minor  common  chords 36 

LXXXIII.    Diatonic  auxiliary  sounds  between  the  various  sounds  of  major 

common  chords 36 

LXXXIV.   The  same  inverted  . 37 

LXXXV.   The  same  applied  to  minor  common  chords 37 

LXXXVI.    Chromatic  auxiliary  sounds  between  the  various  sounds  of  major 

common  chords 37 

LXXXVII.   The  same  inverted  . 38 

LXXXVIII.   The  same  applied  to  minor  common  chords 38 

LXXXIX.    Diatonic  auxiliary  sounds  applied  to  the  dominant  and  tonic 

harmonies  of  major  keys 39 

XC.   The  same  in  minor  keys 39 

XCI.    Chromatic  auxiliary  sounds  applied  to  the  dominant  and  tonic 

harmonies  of  major  and  minor  keys 39 

XCII.    Diatonic  auxiliary  sounds  applied  to  the  subdominant,  dominant 

and  tonic  harmonies  of  major  keys 40 

XCIII.   The  same  in  minor  keys 40 

XCIV.    Chromatic  auxiliary  sounds  applied  to  the  subdominant,  domi- 
nant and  tonic  harmonies  in  major  and  minor  keys      ...  40 

XCV.    Diatonic  auxiliary  sounds  approached  by  leap 41 

XCVI.    Basic  harmonies  for  examples  of  diatonic  auxiliary  sounds  ap- 
proached by  leap 41 

XCVII.    Chromatic  auxiliary  sounds  approached  by  leap 42 

XCVIII.    Basic  harmonies  for   examples  of  chromatic   auxiliary  sounds 

approached  by  leap 42 

XCIX.   Accented   diatonic   auxiliary   sounds   applied   to   major   com- 
mon chords 43 

C.   The  same  inverted      43 

CI.    The  same  applied  to  minor  common  chords 43 

CII.   Accented  chromatic  auxiliary  sounds  applied  to  major  common 

chords _ 43 

CII  I.   The  same  applied  to  minor  common  chords 43 

CIV.    Basic    harmonies    for    melodies    containing   accented    diatonic 

auxiliary  sounds 44 

CV.   The  same,  including  chromatic  auxiliary  sounds 44 

CVI.   The  simultaneous  combination  of  harmonic  and  auxiliary  sounds 

in  connection  with  single  common  chords 45 

CVII.   The  same  applied  to  the  harmonies  of  the  dominant  and  tonic.  45 

CVIII.    Basic  harmonies  for  the  further  exemplification  of  the  same       .  46 

CIX.   Changing-notes 46 


Index  to  the  Steps 


xv 


STEP 


SUBSTANCE 


PAGE 


CX.   The  improvisation  of  progressions  in  major  keys,  ending  with  a 

full  close 50 

CXI.   The  same  in  minor  keys " 50 

CXII.   The  improvisation  of  progressions  in  major  keys,  ending  with  the 

semi-final  perfect  cadence 51 

CXIII.   The  same  in  minor  keys 51 

CXIV.   The  improvisation  of  progressions  in  major  keys,  ending  with  the 

inverted  perfect  cadence 51 

CXV.   The   same    in    minor    keys * 51 

CXVI.   The  improvisation  of  progressions  in  major  keys,  ending  with 

the  subdominant-tonic  cadence 51 

CXVI  I.   The  same  in  minor  keys 52 

CXVIII.   The  improvisation  of  progressions  in  major  keys,  ending  with  the 

subdominant-tonic  cadence  in  inverted  form 52 

CXIX.   The  same  in  minor  keys 52 

CXX.   The  improvisation  of  progressions  in  major  keys,  ending  with  the 

harmony  of  the  dominant 53 

CXXI.    The  same  in  minor  keys 53 

CXXII.  The  improvisation  of  progressions  in  major  keys,  ending  with 
the  second  inversion  of  the  tonic  and  the  dominant  har- 
mony    53 

CXXIII.    The  same  in  minor  keys 53 

CXXIV.  The  improvisation  of  two  phrases,  the  first  closing  with  a  domi- 
nant cadence 54 

CXXV.   The  same  in  minor  keys 54 

CXX VI.   The  improvisation  of  progressions  in  major  keys,  ending  with 

an  interrupted  cadence 55 

CXXVTI.    The  same  in  minor  keys 55 

CXXVIII.   The  improvisation  of  two  phrases  in  major  keys,  the  first  closing 

with  an  interrupted  cadence      55 

CXXIX.   The  same  in  minor  keys 55 

CXXX.    Experiments  in  the  less  usual  forms  of  cadence 56 

CXXXI.    The  improvisation  of  three  phrases  with  diverse  cadences  ...  57 

CXXXII.   The  improvisation  of  complete  musical  thoughts 57 

CXXXIII.   The  linking  of  a  major  common  chord  to  another  chord  without 

respect  to  key  . * 58 

CXXXIV.   The  decoration  of  the  same       58 

CXXXV.   The  linking  of  a  minor  common  chord  to  another  chord  without 

respect  to  key 60 

CXXXVI.   The  decoration  of  the  same       60 

CXXXVII.   The  linking  of  three  chords  without  respect  to  key 60 

CXXXVIII.   The  decoration  of  the  same       60 

CXXXIX.   The  linking  of  three  chords  with  reference  to  key 62 

CXL.   The  decoration  of  the  same       62 

CXLI.    Chordal  transference  from  major  common  chords  in  reference 

to  change  of  key 63 

CXLI  I.   The  same  from  minor  common  chords 64 

CXLIII.   Chords  common  to  two  keys 64 

CXLIV.   Sequences  formed  from  figures  of  two  chords 66 

CXLV.   Sequences  formed  from  models  of  more  than  two  chords     ...  67 

CXLVI.    Non-uniform  sequences 67 

CXLVII.   The  sequence  as  a  means  of  modulation 68 

CXLVIII.   Pedals 70 


XVI 


Index  to  the  Steps 


STEP 


SUBSTANCE 


PAGE 


CXLIX.    Progressions  ending  with  a  chromatic  harmony 72 

CL.   The  same  in  minor  keys 72 

CLI.    Progressions  ending  with  a  chromatic  chord  affiliated  to  the 

previous  harmony 73 

CLI  I.   The  same  in  minor  keys 73 

CLIII.    Progressions  starting  with  a  chromatic  harmony 74 

CLIV.   The  same  in  minor  keys 74 

CLV.   The  processes  of  Steps  CXLIX  and  CLIII  combined 74 

CLVI.    The  same  in  minor  keys 74 

CLVII.   The  use  of  the  dominant  7th  in  closely-related  keys 76 

CLVIII.   The  same  in  minor  keys 76 

CLIX.   The  appropriation  of  the  dominant  7th  in  remote  keys   ....  76 

CLX.   The  chord  of  the  augmented  6th  on  the  minor  6th  of  major  keys  78 

CLXI.   The  same  in  minor  keys     . 79 

CLXII.   The  chord  of  the  augmented  6th  on  the  minor  2nd  of  major  keys  79 

CLXIII.   The  same  in  minor  keys 79 

CLXIV.   The  building  of  the  entire  dominant  discord      80 

CLXV.   The  combination  of  the  root,  3rd,  7th,  and  9th  of  the  dominant 

discord  in  major  keys 81 

CLXVI.   The  same  in  minor  keys 82 

CLXVII.   The  combination  of  the  root,  5th,  7th,  and  nth  of  the  dominant 

discord       82 

CLXVIII.   The  combination  of  the  root,  3rd,  7th,  and  I3th  of  the  dominant 

discord  in  major  keys 82 

CLXIX.    The  same  in  minor  keys 82 

CLXX.   The  alternate  use  of  the  variable  members  of  the  dominant  dis- 
cord      82 

******* 

CLXXI.    Enharmonic  change  effected  by  a  single  sound      83 

CLXXII.   The  succession  of  chords  of  the  diminished  7th 85 

CLXXI II.    Modulation  by  means  of  the  chord  of  the  diminished  7th  ...  85 
CLXXIV.   The  enharmonic  contrast  between  the  chords  of  the  dominant 

7th  and  augmented  6th       86 


HARMONY  IN  PIANOFORTE-STUDY 


PART   I 

Plain    Harmony 


STEP  I.  —  Play  any  of  the  twelve  major  common  chords  in  the 
root-position,  each  chord  selected  to  exhibit  several  varieties  of 
sound-distribution.  (Ex.  I.) 


Ex. 

A. 

n 

. 
B. 

c. 

i 

D. 

L/ 

1       j*^ 

1     S 

J§        l 

«o             II 

/L 

c* 

1 

1 

II 

KB 

1      i 

1    S 

1 

S            || 

\>\)         H 

1    C 

(^        • 

H 

c/          ^ 

3. 

£^v  .           **^^ 

|(? 

1 

"         1 

^            II 

1  •          4f^7 

E 

1-2 

S            II 

^            '    -^ 

5 

1 

9           1 

^            II 

Note  i.  —  77^  diatonic  scale  affords  a  certain  clue  to  the  formation 
of  any  common  chord.  Before  proceeding  to  the  chords  of  Step  I,  the 
student  should  therefore  play  one  octave  of  the  scale  belonging  to  each  of 
the  major  keys  selected.  The  ist,  jrd,  and  $th  degrees  of  the  scale 
determine  the  pitch  of  the  sounds  which  form  the  common  chord  of  the 
tonic. 

Note  2.  —  The  common  chord  contains  but  three  sounds;  conse- 
quently, additional  units  or  parts  can  be  obtained  only  by  repeating  or 
doubling  one  or  more  of  these  sounds.  It  is  in  this  way  that  the  added 
sounds  in  Ex.  I  are  obtained. 

Note  3.  —  In  vocal  writing,  the  number  of  sounds  in  a  chord  is 
determined  by  the  number  of  the  voice-parts.  No  limitation  of  the 
kind  exists  in  the  case  of  chords  intended  for  instrumental  expression. 

Note  4.  —  All  chordal  positions,  in  which  the  sounds  are  not  indi- 
vidually perceptible  to  the  ear,  should  be  avoided.  Ex.  2,  A ,  is  ineffec- 
tive because  of  the  closeness  of  position  assigned  to  the  three  lowest 
sounds.  The  elimination  of  the  lower  3rd,  as  in  B,  effects  an  im- 
mediate improvement. 


Harmony  in  Pianoforte-Study 


Ex.2. 


Note  5.  —  TVfe  sounds  of  a  c^orrf  should,  under  ordinary  circum- 
stances, be  distributed  at  approximately  equal  distances.  If  any 
pronounced  interval  exist  between  one  sound  and  another,  this  should, 
as  a  rule,  be  arranged  between  the  bass  sound  and  the  sound  next  above. 
Such  a  separation  of  the  bass  sound  from  the  tipper  sounds  is  par- 
ticularly desirable  when  a  chord  is  played  at  a  low  pitch.  Thus,  Ex.  2, 
B,  played  an  octave  lower,  creates  a  species  of  aural  confusion;  on  the 
other  hand,  Ex.  2,  A ,  played  an  octave  higher,  is  perfectly  effective. 

Note  6.  —  In  the  next  Step  the  student  will  learn  how  to  present  a 
simple  chord  in  decorated  form.  It  will  therefore  be  interesting  and 
helpful  first  to  play  an  example  of  such  embellishment  by  a  classic 
master.  (Ex.  j.) 


Ex.  3. 

Allegro  con 


BEETHOVEN.     Sonata,  Op.  2,  No.  3. 


STEP  n.  —  Treat,  decoratively,  any  of  the  twelve  major  common 
chords  in  the  root-position:  (a)  By  chords  presented  in  the  form  of 
figures,  (Ex.  4);  or  (b)  by  well-defined  passages  of  broken  chords 
(Ex.  5)- 

Ex.4. 

Leggiero. 


Plain  Harmony 


Ex.5. 


Allegretto. 


Note  7.  —  In  the  above  examples,  it  is  necessary  fully  to  appreciate 
the  composite  nature  as  well  as  the  entire  co-relationship  and  kinship 
of  the  various  sounds.  It  is  of  equal  importance  that  the  ear  should 
realize  the  influence  of  the  root  throughout.  Ex.  6  is  another  version  of 
Ex.  5,  and  illustrates  the  importance  of  the  part  played  by  the  piano- 
forte pedal  in  passages  of  the  kind.  In  this  case  the  pedal  retains  the 
root  of  the  chord  throughout. 


Ex.  6. 


rj.o  , 

j    • 

\                     ^11 

EZ  A   h^- 

5a 

X3                                                                             X3                 ^        1 

Ped. 


'-I 


Note  8.  —  r/te  ac/  of  presenting  a  chord  in  decorative  form  is  not 
completed  by  the  mere  succession  of  the  sounds  in  the  shape  of  figures, 
chordal  or  otherwise.  Something  more  is  required  before  such  a  pas- 
sage can  be  said  to  be  invested  with  musical  significance.  It  is  a  first 
condition  of  success  that  the  grouped  figures  should  be  presented  in 
rhythmic  form;  Ex.  6  is  a  clearly  cut  rhythm  of  four  bars.  A  second 
and  very  important  condition  is  that  the  problems  of  stress  and  repose 
should  receive  careful  consideration;  Ex.  6  is  represented  as  demanding 
a  gradually  increasing  stress.  The  third  condition  almost  claims 
priority  by  insisting  upon  the  expression  of  each  progression  in  some 
definite  form  of  time;  the  examples  just  given  fulfil  this  condition  in 
each  case.  In  brief,  the  student  must  not  allow  himself  to  ramble  amid 
an  incoherent  maze  of  sounds;  on  the  contrary,  before  reproducing  his 
conception  upon  the  instrument,  he  must  cultivate  the  power  mentally 
to  conceive  the  type  of  progression  which  he  desires  to  express.  It 
should  be  his  aim  to  set  each  example  in  a  thoroughly  musical  and 
attractive  environment. 

Note  9.  —  Much  can  be  achieved  in  the  decorative  expression  of  a 
common  chord  aided  only  by  the  elements  of  time,  accent,  and  rhythm; 


Harmony  in  Pianoforte-Study 


to  which  must,  of  course,  be  added  emotional  conception.     Ex.  7  is  a 
complete  musical  thought  founded  upon  a  single  chord  of  the  kind. 

Ex.7.* 

Maestoso.  _ 


•&- 


4 


H 


:£ 


f        *    • 

i-.        -4.  -•-. 


STEP  in.  —  Play  examples  of  first  inversions  of  any  of  the  twelve 
major  common  chords.  Each  chord  should  be  presented  in  various 
positions,  the  3rd  being  in  every  case  the  lowest  sound.  (Ex.  8.) 


Ex.  8. 


II        1 

5         1 

Z           || 

5 

a      1 

1 

; 

3 

51         1 

II 

o        c/              <» 

1 

22. 

a. 

r>*       r^        EZm& 

Is 

| 

(?         ii 

1        i 

1 

II 

Z  "  •"«'               ^ 

E 

Z 

«-         II 

Note  10.  —  Step  III  illustrates  the  importance  of  listening  to  the 
bass  sound  of  a  chord.  In  a  very  particular  sense,  the  bass  is  the  most 
virile  member  of  any  chordal  combination;  and  it  is  not  too  much  to 
add  that  the  harmonic  instinct  is  strong  in  proportion  as  the  fundamental 
sounds  of  harmony  are  continuously  perceptible  to  the  inward  sense.  . 


*  An  approximation  of  a  treatment  played  to  the  author  by  one  of  his  younger  students. 


Plain  Harmony  $ 

Note  ii.  —  When  the  3rd  of  a  major  common  chord  is  in  the  bass  — 
as  in  the  case  of  a  first  inversion  —  it  is  usually  ineffective  to  repeat  it 
in  another  part  except  as  an  octave  to  the  bass.  —  Ex.  g,  A,  is  unpleas- 
ing;  but  this  is  avoided  in  B  by  the  alteration  in  the  uppermost  part. 


Ex.  9. 

A. 

A 

B. 

u 

If            .- 

1    E2 

A.       \\9 

1  K 

ftv   .  u&> 

HtH 

^K  b  fz 

1      fv.;, 

-<9- 

-&- 

£™V  • 

- 

*J                   ^ 

STEP  IV.  —  Apply  simple  forms  of  decoration  to  any  of  the  first 
inversions  of  the  twelve  major  common  chords.     (Ex.  10.) 
Ex.  1O. 

Brillante. 


Note  12.  —  /«  //fw  5^/>,  it  is  very  necessary  to  ensure  that  the  jrd 
of  the  chord  be  heard  throughout  the  passage  as  the  lowest  sound.  As 
a  rule,  the  pedal  should  be  used  to  retain  this  sound.  (Cf.  Notes  7 
and  /o.) 


STEP  V.  —  Play  examples  of  second  inversions  of  major  common 
chords;  each  chord  to  be  presented  in  various  positions,  the  5th  being 
in  every  case  the  lowest  sound.  (Ex.  n.)  The  substance  of  Note 
10  should  be  recalled  at  this  point. 


*="T* 


D. 


Harmony  in  Pianoforte-Study 


STEP  VI.  —  Apply  decorative  forms  to  the  chords  of  Step  V. 
(Ex.  12.) 

Ex.   12. 

Leggier o. 


i 


i 


i 


S 


ic 

m.  Ped 

^   *     ww. 


Fed. 


STEP  VII.  —  Play  examples  of  the  twelve  minor  common  chords 
in  the  root-position.  By  omitting  the  sharp,  Ex.  i  may  be  translated 
into  the  tonic  minor  for  illustration. 

Note  13.  —  The  minor  common  chord  should  be  built  up  from  the 
1st,  3rd,  and  $th  sounds  of  the  minor  scale.  (Cf.  Note  i.) 


STEP  VIII.  —  Treat,  decoratively,  any  of  the  twelve  minor  com- 
mon chords  in  the  root-position.  (Cf.  Exs.  4  and  5  translated  into 
the  tonic  minor  by  the  substitution  of  a  minor  3rd.) 

****** 

STEP  IX.  —  Play  examples  of  the  first  inversions  of  minor  common 
chords.  (Cf.  Ex.  8  translated  into  the  minor  by  the  alteration  of 
the  3rd  in  the  bass.) 

Note  14.  —  The  substance  of  Note  n  should  be  remembered  in  con- 
nection with  the  chords  of  this  Step.  Regarded  generally,  however,  the 
indiscriminate  doubling  of  the  bass  sound  is  less  objectionable  in  the 
case  of  first  inversions  of  minor  common  chords. 


STEP  X.  —  Apply  decorative  forms  to  the  chords  of  Step  IX. 
(Cf.  Ex.  10  translated  into  the  tonic  minor.) 


STEP  XI.  —  Play  examples  of  second  inversions  of  minor  com- 
mon chords.     (Cf.  Ex.  n  translated  into  the  tonic  minor.) 


STEP  XII.  —  Apply  decorative  forms  to  the  chords  of  Step  XL 
(Cf.  Ex.  12  translated  into  the  tonic  minor.) 


Plain  Harmony 

STEP  XIII.  —  Having  played  one  octave  of  any  one  of  the  twelve 
major  scales  (Ex.  13,  A),  sound  the  dominant  common  chord  of  that 
key 


Ex.   13. 

A. 


B. 


i 


Y-    fc^I » g     IT      TT  H 

-<S>-       2?"  ff 

Note  15.  —  TVze  chords  treated  in  Steps  I  to  XII  are  presumed  to 
be  of  a  tonic,  and  therefore  of  a  final,  nature.  The  effect  of  finality  is 
disturbed  by  playing  the  scale  of  the  key  before  sounding  the  chord  of 
the  dominant,  and  the  difference  between  a  chord  of  completion  and  one 
of  incompletion  becomes  clear  to  the  aural  sense.  A  realization  of  the 
restless  character  of  the  dominant  harmony,  and  the  satisfaction  it 
invariably  finds  in  that  of  the  tonic,  lies  at  the  root  of  all  harmonic  per- 
ception and  endeavour. 


STEP  XIV.  —  Play  the  common  chords  of  the  dominant  and  tonic 
in  various  major  keys.  The  chords  should  be  played  individually 
after  the  manner  of  Ex.  14. 


Note  1 6.  —  Step  XIV  is  a  necessary  prelude  to  Step  XV.  It  is 
not  intended  that  the  chords  should  be  regarded  as  forming  one  progres- 
sion, but  that  the  student  should  be  thoroughly  well  informed  as  to  the 
tonal  position  of  the  harmonies  which  he  will  presently  be  required  to 
play  in  harmonic  combination. 

N.B.  —  The  chords  of  this  Step  should  not  be  played  in  decorative 
form. 


STEP  XV.  —  Play,  in  harmonic  succession,  the  dominant  and  tonic 
chords  of  various  major  keys.  (Ex.  15.)  The  chords  should  be 
attempted  in  as  many  positions  as  possible  and  the  strength  of  the 
movement  of  the  bass  part  from  dominant  to  tonic  carefully  ob- 
served. (Cf.  Note  10.) 


Ex.  15. 
A. 


Harmony  in  Pianoforte-Study 

B.  C. 


yK  2   "* 

—  ^  H 

/Tfvo  —  ^1  

~~F  —  H 

\MJ^5     "* 

X       II 

O            ^                l^' 

C"~\  .  &)     (%} 

e* 

M  *  *— 

._  „ 

Z   o 

^         1 

25 

II 

Note  17.  —  Experiment  will  prove  that  the  best  effects  are  produced 
when  the  uppermost  sounds  remain  the  same  in  both  chords,  or  move 
but  a  2nd  from  the  first  chord  to  the  next.  Both  types  appear  in  Ex. 
15.  A  is  clearly  more  monotonous  than  either  B  or  C.  B  is  the 
strongest  or  most  conclusive  progression.  The  upward  movement  of 
the  top  part  of  C  to  the  3rd  of  the  tonic  harmony  offers  more  freedom 
from  the  commonplace  than  if  it  descended  to  the  root. 

Note  18.  —  The  student  whose  harmonic  knowledge  has  been  re- 
stricted to  vocal  part-writing  will  here  be  inclined  to  permit  any  power 
he  may  have  gained  to  dominate  his  presentation  of  chords  upon  the 
pianoforte.  When  writing  for  voices,  it  is  not  only  indispensable  that 
the  parts  should  be  clearly  individualized,  but  that  the  movement  of  each 
part  should  be  perceptible  to  the  ear.  On  the  other  hand,  when  writing 
for,  or  expressing  harmonic  progressions  upon,  the  pianoforte,  it  is  the 
effect  of  the  chord  in  the  mass  which  usually  counts,  and  no  restriction 
may  be  held  to  exist  as  regards  the  movement  and  treatment  of  the  vari- 
ous members  of  each  chord  save  those  which  are  imposed  by  good  sense 
and  musicianly  effect. 

Note  19.  —  Extended  positions  of  the  chords  may  be  obtained  effec- 
tively by  an  intelligent  use  of  the  pedal.  (Ex.  16.) 

Ex.   16. 
A. 


Fed. 


*Ped.* 


Fed. 


#Ped. 


STEP  XVI.  —  Apply  simple  forms  of  decoration  to  the  dominant 
or  tonic  chords  or  to  both.  Ex.  17,  A  and  B,  illustrate  such  em- 
bellishment by  means  of  a  chordal  figure;  C  and  D,  by  the  use  of 
the  arpeggio. 


Plain  Harmony  9 

Note  20.  —  //  will  be  found  advisable  first  to  sound  the  tonic  chord 
of  each  key  before  proceeding  to  the  complete  progression;  and  this  prac- 
tice should  be  adopted  generally  in  all  future  combinations. 


Ex.  17. 

A. 


B.    Lusingando. 


S 


\ 


g 


Fed. 


*Ped. 


Ped. 


D.     Brillante. 


Ped. 


* 

Ped.  * 


10 


Harmony  in  Pianoforte-Study 


Note  21.  —  In  the  act  of  presenting  harmonies  in  the  florid  manner 
above  set  forth,  care  should  be  taken  mentally  to  preserve  the  original 
shape  of  the  chord  or  chords  embellished.  At  this  stage,  each  arpeggio 
should  be  formed  from  a  chord  which,  throughout  the  process  of  embel- 
lishment, is  clearly  perceived  by  the  inward  sense.  For  example,  the 
original  design  of  each  chord  embellished  in  Ex.  18,  A,  is  outlined 
in  B. 


Ex.  18. 

A.    A  llfgretto 


BEETHOVEN.     Sonata,  Op.  31,  No.  2,  3rd  mov. 


:8: 


STEP  XVII.  —  Repeat  the  progression  of  Step  XV  many  times 
consecutively,  exemplifying  the  chords  in  a  new  position  at  each 
repetition.  (Ex.  19.) 


Plain  Harmony 


II 


Ex.  19. 


Fed.*     Ped.^t     simile. 


8 


STEP  XVm.  —  Improvise  short  melodies  in  the  major  keys,  the 
last  two  sounds  of  which  will,  in  each  case,  provide  a  position  for 
the  introduction  of  the  progression  demonstrated  in  Step  XV. 
(Exs.  20  and  21.) 


Ex.  2O. 

Soavemente. 

Q 

-" 

-                       ^ 

^T 

Jf  u(j  —  f  — 

P                   0 

9 

"P  •  1  J 

,j  .  

—  ^    N  H   II 

CcT)  F 

1       {. 

P  ^-* 

1 

*.     kj    n   II 

*  —  V  —  l 

P 

IX  ^^"^^ 

"I 

B  *<r,* 

r-v.     j 

^ 

i  —  ^~ 

X   1    • 

:  • 

Ex.  21. 


Note  22.  —  Step  XVIII  represents  the  beginning  of  musical  self- 
expression,  and  is  therefore  of  great  importance.  It  is  at  this  stage  that 
the  real  function  of  harmony,  the  mission  of  the  cadence,  and  the  in- 
fluence of  the  latter  upon  rhythmic  expression,  become  clear  to  the  mu- 
sical sense. 


STEP  XIX.  —  Having  played  one  octave  of  any  harmonic  minor 
scale,  sound  the  dominant  common  chord  of  the  same  key.  (Cf. 
Step  XIII.) 


12  Harmony  in  Pianoforte-Study 

STEP  XX.  —  Play,  in  harmonic  succession,  the  common  chords 
of  the  dominant  and  tonic  in  various  minor  keys.  The  chords 
should  be  attempted  in  a  large  variety  of  positions.  (Cf.  Ex.  15 
translated  into  the  tonic  minor  by  substituting  a  minor  3rd  in  the 
tonic  harmony.) 

Note  23.  —  It  is  more  difficult  for  the  average  student  to  appreciate 
tonality  in  the  minor  key.  It  is  therefore  helpful  first  to  express  the 
two  chords  in  connection  with  the  complete  scale.  (Cf.  Exs.  15  and  22.) 

Ex.  22. 


V 

1  1 

/f 

b        &     ^     II 

|(T\                                   , 

^•K                           aSa        f 

?          &                       <5"       br?          1  1 

D       _,£,_     o    yfi? 

^i       [/&< 

c\- 

•")• 

II 

& 

« 

Note  24.  —  It  is  most  important  to  observe  that  the  harmony  of  the 
dominant  is  major  in  both  modes,  major  and  minor.  (Cf.  Exs.  15 
and  22.) 


STEP  XXI.  —  Apply  forms  of  embellishment  to  the  progressions 
of  Step  XX.     (Cf.  Ex.  17.) 


STEP  XXII.  —  Repeat  the  progressions  of  Step  XX  many  times 
consecutively,  exemplifying  the  chords  in  a  new  position  at  each 
repetition.  (Cf.  Step  XVII.) 


STEP  XXIII.  —  Improvise  short  melodies  in  the  minor  keys,  the 
last  two  sounds  of  which  will,  in  each  case,  introduce  the  progression 
exemplified  in  Step  XX.  (Ex.  23.) 


Ex.  23. 

Affetttioso. 

r\     i                  -  —                          "~^ 

'  — 

"^ 

—                 ^~*^~ 

\j  ,  ™  o    i      r3       f 

fy 

^\P  bo    j       | 

—  * 



F  

>-===> 

—        —=r: 

—    —  
—    .  

^M                          w 

1 

r^v  •       l_    6"J 

• 

^-                     1  1 

1  •    17  i!                      — 

*-— 

1  1 

^—9-\}Q  

I  5i  |J 

Plain  Harmony 


STEP  XXIV.  —  Having  played  one  octave  of  a  major  scale  (Ex. 
24,  A),  sound  the  subdominant  common  chord  of  the  same  key  (B). 


Ex.  24. 
A. 


V- 


B. 

JO.. 


Note  25.  —  The  student  is  here  directed  aurally  to  examine  a  chord 
which  occasionally  supplants  the  dominant  harmony  in  a  final  cadence. 
It  will  be  helpful  to  alternate  Step  XIII  with  Step  XXIV;  similarly, 
Step  XV  with  Step  XXV. 


STEP  XXV.  —  Connect  the  common  chords  of  the  subdominant 
and  tonic  in  any  of  the  twelve  major  keys.     (Ex.  25.) 


Note  26.  —  In  the  above  examples,  the  strength  of  the  movement  of 
the  bass  part  should  be  observed  experimentally  and  comparison  made 
with  the  same  feature  in  the  progressions  of  Ex.  15.  Here,  also,  the 
best  effects  will  be  obtained  by  the  player  when  the  top  part  remains  the 
same  in  both  chords  (B),  or  moves  but  a  2nd  from  one  to  the  other  (A 
and  C).  (Cf.  Note  17.) 


STEP  XXVI.  —  Reproduce  the  progressions  of  Step  XXV  in  em- 
bellished form. 


STEP  XXVII.  —  Repeat  the  progressions  of  Step  XXV  many 
times  consecutively,  playing  the  chords  in  a  new  position  at  each  repe- 
tition. (Ex.  26.) 


Harmony  in  Pianoforte-Study 


Ex.  26. 

Allegretto. 


STEP  X3CV1II.  —  Improvise  short  melodies  in  the  major  keys,  the 
last  two  sounds  of  which  will,  in  each  case,  provide  a  position  for 
the  chords  of  the  subdominant  and  tonic.  (Ex.  27.) 


Ex.  27. 

Placido. 

(fK"^o              b       J  •    ^    ** 

IP  —  -J  1  '-I 

^=0 

^ 

*^F 

1 

"l  •        II 

1 

^~"V  •        I—     jl 

_J          M 

»        ..  .1         v             ^ 

«  •   ... 

STEP  XXIX.  —  Having  played  one  octave  of  a  minor  scale  in  the 
harmonic  form,  sound  the  subdominant  common  chord  of  the  same 
key.  (Cf.  Ex.  24.) 

Note  27.  —  .4  grea/  difference  between  the  dominant  and  subdominant 
harmonies  is  observable  in  the  respective  modes.  Unlike  the  former,  the 
chord  of  the  subdominant  varies  with  the  mode,  being  a  major  chord  in 
the  major  key  and  a  minor  chord  in  the  minor  key.  An  (Esthetic  vari- 
ation of  this  type  should  be  appreciated  aurally  to  the  fullest  extent, 
and  for  this  purpose  Step  XXIX  should  be  alternated  with  Step 
XXIV. 


STEP  XXX.  —  Combine  the  common  chords  of  the  subdominant 
and  tonic  in  various  minor  keys.  (Cf.  Ex.  25  translated  into  the 
tonic  minor  by  substituting  minor  thirds  in  both  chords.) 


STEP  XXXI.  —  Reproduce  the  progressions  of  Step  XXX  in  deco- 
rated form.     (Ex.  28.) 


Plain  Harmony 


Ex.  28 


Fed. 


STEP  XXXIE.  —  Repeat  the  progression  of  Step  XXX  many  times 
consecutively,  playing  the  chords  in  a  new  position  at  each  repeti- 
tion. (Cf.  Step  XXVII.) 


STEP  XXXIII.  —  Improvise  short  melodies  in  the  minor  keys,  the 
last  two  sounds  of  which  will,  in  each  case,  introduce  the  progression 
referred  to  in  Step  XXX.  (Ex.  29.) 


Ex.  2$ 

j 

nti 

3. 

btafo. 

•^                                                                                                                                                           ^ 

L/tfo 

/L  *• 

fv          1 

> 

s 

vT)  4- 

• 

J        g 

i               C         i 

«       wj 

-  .          a         m 

•  •          J 

/* 

^^                         *    ^ 

1 

r~x  •  ft) 

II 

I  •  *f  f  J                                ^^m 

— 

if        ^             • 

f>,        •+      II 

-S    'A 

B       «^ 

E 

STEP  XXXIV.  —  Combine,  in  various  major  keys  and  in  one  un- 
broken progression,  the  common  chords  of  the  subdominant,  domi- 
nant and  tonic  in  the  order  given.  The  chords  should  be  played  in 
as  many  positions  as  possible.  Great  variety  in  melodic  movement 
should  also  be  attempted.  Ex.  30  illustrates  two  of  many  possibili- 
ties. 


Ex.  3O. 

A. 

'«(?'•*•            1 

L/  .  !/  o       j 

II         / 

I/  1  ™  O          (^                    ^j 

—  —  H 

/^\P  b^      /v 

^ 

I  

=^=1 

(foP|?g          ^            =g= 

~^  —  H 

w 

1  ! 

1  ,5)  II          ) 

"**"•              ^ 

^    rti.O        _, 

^=\\ 

^=n 

i6 


Harmony  in  Pianoforte-Study 


Note  28.  —  //  may  be  pointed  out  that,  in  progressing  from  the  sub- 
dominant  to  the  dominant  chords,  the  best  results  are  obtained  when  the 
upper  parts  proceed  in  contrary  movement  to  the  bass  part.  This  is 
the  case  in  each  of  the  above  examples. 

Note  29.  —  The  chords  of  the  subdominant,  dominant  and  tonic 
should  also  be  treated  intensively  after  the  manner  of  Exs.  19  and  26; 
and  this  procedure  may  be  followed  with  advantage  in  the  remaining 
Steps  of  this  Part. 


STEP  XXXV.  —  Treat,  decoratively,  the  progressions  of  Step 
XXXIV.  The  embellishment  may  be  in  chordal  form  (Ex.  31)  or  in 
arpeggio-form.  (Ex.  32.)  In  all  cases  the  tonic  chord  should  first 
be  sounded.  (Cf.  Note  20.) 


Ex.  31. 


Leggiero. 


^ 


% 


Ex.  32. 

Con  moto. 


Plain  Harmony  17 

STEP  XXXVI.  —  Improvise  short  melodies  in  various  major  keys, 
the  last  three  sounds  of  which  will,  in  each  case,  provide  a  position 
for  the  chords  of  the  subdominant,  dominant  and  tonic.     (Ex.  33.) 
Ex.  33. 


/kt>tT}|  



-*— 

q  — 

~fe~~:  

L/ 

i/      1 

j^^Jj    N  rgi-i- 

J. 

-&-• 

rv 

iS 

rfr.Btr 
EESS 

-*  f~ 

—  *  — 

3E 

STEP  XXXVII.  —  Combine,  in  various  minor  keys  and  in  one  un- 
broken progression,  the  common  chords  of  the  subdominant,  domi- 
nant and  tonic.  (Cf.  Ex.  30  translated  into  the  tonic  minor  by 
substituting  a  minor  3rd  in  the  first  and  last  chords.)  The  chords 
should  be  presented  in  as  many  positions  as  possible  and  great  variety 
of  melodic  movement  attempted. 

Note  30.  —  The  combination  given  in  this  Step  should  be  compared 
carefully  and  experimentally  with  the  same  combination  in  the  major 
mode.  (Step  XXXIV.)  In  the  major  key,  the  chord  of  the  dominant 
stands  between  two  major  chords;  in  the  minor,  it  is  between  two  minor 
chords.  Nevertheless,  it  must  be  clear  aurally  that  the  bass  part  —  IV, 
V,  I  —  is  the  same  in  either  case.  The  tonic,  dominant  and  subdomi- 
nant, or  the  three  primary  members  of  tonality,  are  invariable  both  in 
the  major  and  in  the  minor. 

STEP  XXXVIII.  —  Treat,  decoratively,  the  progressions  of  Step 
XXXVII.  (Cf.  Exs.  31  and  32.) 

****** 

STEP  XXXIX.  —  Improvise  short  melodies  in  various  minor  keys, 
the  last  three  sounds  of  which  will,  in  each  case,  provide  a  position 
for  the  chords  of  the  subdominant,  dominant  and  tonic.  (Ex.  34.) 


Ex.  34. 

Grazioso. 

tfTTf^^ 

^=^\ 

\  '  r  rf  •  •  *  -  ' 

m*  *-*?— 

*  —  P^- 

t=t^ 

i»: 

Tf?!~ 

ucr  ;•  —  ' 

^ 


i8 


Harmony  in  Pianoforte-Study 


STEP  XL.  —  Having  played  one  octave  of  a  major  scale  (Ex.  35, 
A),  sound  the  common  chord  of  the  supertonic  (B). 


Ex.  35. 
A. 


a 


Note  31.  —  In  the  chord  of  the  supertonic  —  a  minor  chord,  as  will 
be  observed  —  the  student  is  introduced  to  one  of  the  tonal  harmonies 
which,  while  highly  important  as  members  of  the  key,  are  lacking  in 
the  direct  and  positive  effect  peculiar  to  those  of  the  dominant  and  sub- 
dominant.  The  latter  chords,  sounded  in  conjunction  with  the  tonic 
harmony,  provide  the  most  perfect  means  of  tonal  satisfaction.  The 
elementary  student  should  therefore  regard  the  remaining  common 
chords  of  the  scale  as  requiring  the  cooperation  of  the  dominant  chord 
for  their  clear  expression  in  relation  to  key.  The  point  involved  may 
be  expressed  by  a  simple  but  helpful  rule:  —  When  in  doubt,  proceed  to 
the  dominant  harmony. 


STEP  XLI.  —  Form  progressions  in  various  major  keys,  introduc- 
ing the  following  chords  in  the  order  given:  supertonic,  dominant, 
tonic:  (a)  In  plain  form  (Ex.  36,  A);  (b)  in  embellished  form  (B). 


B.    Leggier o. 


Plain  Harmony  19 

Note  32.  —  The  movement  of  the  bass  part  in  the  above  example  — 
//,  V,  I  —  should  be  observed  and  compared  aurally  with  the  same 
feature  of  Ex.  30,  viz.,  IV,  V,  I.  (Cf.  Note  10.)  The  substitution 
of  the  chord  of  the  supertonic  for  that  of  the  subdominant  necessarily 
'widens  the  choice  in  melodic  progression.  The  examples  should  not 
only  be  presented  in  as  many  chordal  positions  as  possible,  but  each 
progression  should  contain  a  different  melodic  outline. 


STEP  XLII.  —  Improvise  short  melodies  in  major  keys,  closing 
with  the  chords  of  the  supertonic,  dominant  and  tonic.     (Ex.  37.) 


Ex.  37. 

Largamente. 

^ 

— 

*  — 

X 

JT     / 

'         r 

•      0 

F  •     • 

1 

^K    t 

•    I         LJ 

r        r 

• 

P  *        • 

•  fT\  / 

1 

r     * 

J 

3 

\>v/ 

V 

25? 

<         mf  -== 
I 

=-  -= 

—  —  — 

kc 

:^~             

^    ^ 

=  —  p 

-JP 

O-^v. 

r^                ^> 

fs           II 

til* 

•^* 

•  — 

^^* 

, 

z  / 

& 

STEP  XLIII.  —  Having  played  one  octave  of  a  major  scale  (Ex. 
38,  A),  sound  the  submediant  chord  of  the  same  key  (B). 


Ex.  38. 
A. 


*=# 


Note  33.  —  >l5  a  secondary  harmony  of  the  key  and,  like  that  of  the 
supertonic,  a  minor  chord,  the  chord  of  the  submediant  is  referred  to 
in  Note  ji,  g_.v. 


STEP  XLIV.  —  Proceed  as  in  Step  XLI,  substituting  the  chord  of 
the  submediant  for  that  of  the  supertonic.  (Ex.  39.)  To  ensure 
correct  tonal  appreciation,  begin,  in  each  case,  by  sounding  the 
harmony  of  the  tonic. 

Ex.  39. 
A. 

•fe- 


^ 


-&- 


Harmony  in  Pianoforte-Study 


Note  34.  —  The  growing  responsibility  attending  the  use  of  new 
chords  and  of  new  chordal  progressions  renders  it  the  more  imperative 
that  the  student  should  be  familiar,  not  only  with  the  characteristic  effect 
of  each  progression  as  a  whole,  but,  in  particular,  with  the  individual 
movements  of  the  respective  bass  parts.  The  bass  movements  of  Ex.  30, 
IV,  V,  I;  of  Ex.  36,  II,  V,  I;  of  Ex.  39,  VI,  V,  I,  should  all  be 
individualized  clearly  by  the  inward  sense. 


STEP  XLV.  —  Improvise  short  melodies  in  major  keys,  closing 
with  the  chords  of  the  submediant,  dominant  and  tonic.     (Ex.  40.) 


Ex.  40. 

Grazioso. 

njf          ^  . 

^"**                     "^ 

f—i  —  1  

tr^  " 

J^  ffffi 

—  — 

r    f 

»— 

t* 

n                     ' 

-1  

-A    * 

(JT)  4  

r 

-\  —  — 

\ 

_^_-f,^_«  «_ 

g    *     1 

*/ 

^^  ^"^^ 

P*     • 
-«=-• 

f"\  •  *fO 

^?     * 

^?     * 

<2                II 

B  *if*  J        ^^* 

•• 

^^* 

Hill 

^     * 

^*     • 

S      | 

•^        vl 

V                          'I 

*     II 

STEP  XLVI.  —  Having  played  one  octave  of  a  major  scale  (Ex. 
41,  .4),  sound  the  common  chord  on  the  mediant  of  the  same  key 


Ex.  41. 

A. 


Note  3$.  —  The  chord  of  the  mediant,  like  those  of  the  submediant 
and  supertonic,  is  a  minor  chord.  It  is  another  of  the  secondary  har- 
monies referred  to  in  Note  31,  q.v. 


Plain  Harmony  21 

STEP  XLVII.  —  Proceed  as  in  Step  XLI,  substituting  the  chord 
of  the  mediant  for  that  of  the  supertonic.  (Ex.  42.)  In  each  case, 
begin  by  sounding  the  chord  of  the  tonic. 


STEP  XLV1I1.  —  Improvise  short  melodies  in  various  major  keys, 
closing  with  the  chords  of  the  mediant,  dominant  and  tonic.  (Ex. 
43-) 

Ex.  43. 

Lento. 


n v  •* i — 


^ 


mf       dim. 


m 


- — *- 


STEP  XLIX.  —  Play  the  chord  of  the  dominant  7th  and  its  inver- 
sions in  various  keys,  major  and  minor.  (Ex.  44.)  Care  must  be 
taken  to  ensure  an  effective  presentation  of  each  chord. 


Ex.  44. 

A.     Root-position. 


1st  inversion. 


2nd  inversion. 
^9-  -OL. 


3rd  inversion. 


3rd  in  bass. 


5th  in  bass. 


7th  in  bass. 


22 


Harmony  in  Pianoforte- Study 


B.     Root-position.  ist  inversion.  2nd  inversion. 


3rd  inversion. 


^==i=FI 

:tirs=u== 


&-fo 


3rd  in  bass.      5th  in  bass. 


7th  in  bass. 


1 


Note  36.  —  The  student  is  here  called  upon  to  appreciate  the  mental 
effect  of  essential  dissonance,  or  that  type  of  dissonance  which  is  an  in- 
tegral and  essential  part  of  a  prevailing  harmony.  The  chords  treated 
hitherto  are  in  every  case  concordant;  but  the  introduction  of  a  dis- 
cordant interval,  such  as  the  ?th  of  Ex.  44,  brings  into  existence  a  chord 
which  requires  the  succession  of  another  harmony  to  satisfy,  to  complete 
or  resolve  the  dissonance  created.  The  process  of  satisfaction,  comple- 
tion, or  —  to  give  the  term  usually  applied  to  it  —  resolution,  is  one  of 
entire  naturalness;  and  it  should  be  particularly  observed  that  the 
movement  of  the  sound  which  forms  the  ?th  is  towards  the  jrd  of  the 
tonic  harmony,  and  that  this  feature  is  operative  in  every  position  or 
inversion  of  the  chord. 


STEP  L.  —  Combine  in  one  progression  the  root-position  of  the 
chord  of  the  dominant  7th  and  the  common  chord  of  the  tonic :  — • 
(a)  In  simple  chordal  form  (Ex.  45,  .4);  (b)  in  decorated  form  (B). 


Fed. 


cresc. 


a 


1 


*Ped, 


STEP  LI.  —  Resolve  upon  the  tonic  harmony,  in  various  keys, 
major  and  minor,  the  first  inversion  of  the  chord  of  the  dominant 
7th: —  (a)  In  plain  form  (Ex.  46,  ^4);  (6)  in  embellished  form  (B). 

Note  37.  —  It  must  be  particularly  observed  that  the  quality  of  dis- 
cordance is  not  impaired  by  the  inversion  of  a  chord  which  contains 
an  essential  dissonance.  The  aural  necessity  properly  to  resolve  the 
7th  in  Exs.  46,  47,  and  48  is  not  less  perceptible  than  in  Ex.  45. 


Ex.  46. 


Plain  Harmony 

Scmplice. 


i 


f*? 

*  * 


-&— 


STEP  LII.  —  Resolve  upon  the  tonic  harmony,  in  various  keys, 
major  and  minor,  the  second  inversion  of  the  dominant  yth: —  (a) 
In  simple  form  (Ex.  47,  A);  (b)  in  decorated  form  (B). 


Ex.  47. 
A. 

Hr-yg- 


fcfc 


B.         Leggieramente. 


Ped. 


*  /'^ 


STEP  LO.  —  Resolve  upon  the  tonic  harmony,  in  various  keys, 
major  and  minor,  the  third  inversion  of  the  dominant  7th :  —  (a) 
In  simple  form  (Ex.  48,  .4);  (b)  in  decorated  form  (B). 


Ex.  48. 
A. 


B.    Pesante. 


^ 


^ 


- 


1 


24  Harmony  in  Pianoforte-Study 

Note  38.  —  It  will  be  remarked  that  attention  to  the  natural  resolu- 
tion of  the  7th  requires  the  last  inversion  of  the  chord  to  be  followed  by 
a  first  inversion  of  the  tonic  harmony.  (Cf.  Note  36.} 

Note  39.  —  The  last  inversion  brings  into  particular  prominence  the 
fact  that  the  original  dissonance  of  the  chord  is  of  a  dual  character. 
Not  only  is  it  the  outcome  of  the  fundamental  and  characteristic  inter- 
val between  the  root  and  the  7th,  but  an  additional  dissonance  is  created 
between  the  3rd  and  7th  in  the  form  of  a  diminished  $th  or  its  inversion, 
an  augmented  4th.  The  individual  effect  of  these  two  discordant  inter- 
vals may  be  appraised  by  playing  in  two  ways  the  chord  given  in  Ex. 
48:  —  (a)  Omitting  the  3rd,  leaving  thus  the  dissonance  of  the  root  and 
7th  only  (Ex.  49,  A);  (b)  omitting  the  root,  the  dissonance  of  the  3rd 
and  7th  alone  remaining  (Ex.  49,  B}.  If  Ex.  48  be  subsequently 
played,  the  greater  richness  of  the  effect  obtained  from  the  union  of  the 
two  dissonances  will  be  clearly  demonstrated. 


Ex.  49. 
A. 

r—Q  :  1 

B. 

JZ. 

&  l_fl  

~~^  M 

•fl\           ^^ 

«                    II 

STEP  LIV.  —  Improvise  short  melodies  in  major  and  minor  keys 
alternately,  the  last  two  sounds  of  which  will  in  each  case  afford  an 
opportunity  for  the  introduction  of  the  dominant  7th  and  its  resolu- 
tion. (Ex.  50.) 

Ex.  5O. 

Con  gusto. 


STEP  LV.  —  Play,  in  various  major  keys,  harmonic  progressions 
composed  of  the  supertonic  common  chord,  chord  of  the  dominant 
7th  and  tonic  chord,  each  in  the  root-position: — (a)  In  chordal 
form;  (6)  in  decorated  form. 


Plain  Harmony  25 

STEP  LVI.  —  Repeat  the  progressions  of  Step  LV,  introducing 
various  inversions  of  the  chords  concerned: —  (a)  In  chordal  form; 
(6)  in  decorated  form.  (Ex.  51.) 


Ex.51. 

Delicate. 

/TN 

r\                     -i 

+  9 

i 

p    - 

U    yf 

—  f-»-s  1 

1 

(S>4  *-"- 

f  i    ' 

=i=b     ^' 

i  •  r  ' 

O                               ^e^« 

3 

^US 

S 

Id  1 

-&- 

f"\*£       0    • 

•  ° 

i 

• 

Z   ' 

Fed. 

#     A*/. 

«•  Ped. 

* 

STEP  LVII.  —  Improvise  short  melodies  in  various  major  keys, 
closing  with  the  progression  referred  to  in  Steps  LV  and  LVI. 


STEP  LVIII.  —  Play,  in  various  major  keys,  progressions  composed 
of  the  submediant  common  chord,  chord  of  the  dominant  7th  and 
tonic  chord,  each  being  in  the  root-position:  —  (a)  In  chordal  form; 
(6)  in  decorated  form. 

****** 

STEP  LIX. —  Repeat  the  progressions  of  Step  LVIII,  introducing 
inversions  of  the  chords  concerned: — (a)  In  chordal  form;  (6) 
in  decorated  form. 


STEP  LX.  —  Improvise  short  melodies  in  various  major  keys, 
closing  with  the  progression  referred  to  in  Steps  LVIII  and  LIX. 
(Ex.  52.) 


Ex.52. 

Piacevole. 


^KJff«!IA^ 

-f8  —  «-f    '  ^   ^ 

h-«h- 

-s>  »— 

-^-f| 

(ft  *4     "^ 

1    r  '   ^  d 

f*   r 

^.^.j  —  ( 

2 

^ 

>> 

-«^*      ~~    -^t        -s-: 

nttA  —  — 

H  

-F  —  H 

\r     if3  

_l  

Ml 

****** 


Note  40.  —  The  two  forms  of  the  minor  scale  known  as  the  harmonic 
and  melodic  illustrate  collectively  the  harmonic  peculiarities  of  the  minor 
key.  Fundamentally,  the  harmonic  form  provides  the  framework  for 


26  Harmony  in  Pianoforte-Study 

the  tonal  harmony;  but  the  variable  degrees  of  the  melodic  form  are 
suggestive  of  further  concords  which  enrich  greatly  the  harmonic  possi- 
bilities of  the  minor  mode. 

STEP  LXI.  —  Having  played  one  octave  of  a  harmonic  minor  scale 
(Ex.  53,  ^4),  sound  the  subdominant  common  chord  of  the  same 
key  (B).  Add  the  harmonies  of  the  dominant  7th  and  tonic,  playing 
the  whole  progression:  —  (a)  In  chordal  form  (C) ;  (b)  in  embellished 
form  (£>). 


Ex.  53. 


C. 


B. 


^- 


-<9- 


D.     Brillante. 


1 


STEP  LXH.  — Proceed  as  in  Step  LXI,  substituting  the  chord  of 
the  submediant  for  that  of  the  subdominant.     (Ex.  54). 

Ex.  54.  C. 


A. 


B. 


m 


BizH2  gZ 

^^=    == 


D.     Grazioso. 


Plain  Harmony 


27 


STEP  LXIII.  —  Improvise  short  melodies  in  various  minor  keys, 
closing  with  either  of  the  progressions  referred  to  in  Steps  LXI  and 
LXII.  (Ex.55.) 


Ex. 

rf#- 

55. 
Giocoso. 

0-    0    f 

9  1 

•  ^3 

bpf 

^g 

0— 

1  —  f~ 

-f^%       *       J. 

j  J  1  i   ^   I    i   ^   M 

\~£¥  —  t 

—  '       lL     -Vn  k- 

>*  I*-  *  ^  ^-  ^ 

P^H  =  

— 

Fed. 


*  Fed.       *  Fed. 


STEP  LXTV.  —  Play  one  octave  of  various  melodic  minor  scales, 
harmonizing  the  last  three  sounds  as  in  Ex.  56. 


Ex.  56. 


i 


i 


P 


Note  41.  —  The  chord  of  the  supertonic  is  represented  in  Ex.  56  as 
formed  upon  the  melodic  form  of  the  scale.  In  this  phase  the  chord  is 
a  common  chord,  and  may  be  used  with  the  absolute  freedom  usual  in 
all  harmonies  of  the  kind. 


STEP  LXV.  —  Play  an  octave  of  the  ascending  form  of  various 
minor  scales,  harmonizing,  in  each  case,  the  last  three  sounds  as 
in  Ex.  57. 


Harmony  in  Pianoforte- Study 


Ex.  57. 


fc^F 

1  ]  H 

~g  —  taH 

—  ^  x  —  f] 

1F    —^  *- 

L-^  —  *  —  ' 

r^  •     j_   o 

0 

s                     II 

V'uvV  

...j?  .  — 

-4  —  *  —  H 

Note  42.  —  The  chord  of  the  supertonic  is  represented  in  Ex.  57  05 
formed  upon  the  harmonic  form  of  the  scale.  In  this  phase  it  is  not 
a  common  chord,  and  requires  to  be  used  with  some  discretion. 


STEP  LXVI.  —  Connect  the  chords  of  the  supertonic,  dominant 
and  tonic  in  various  minor  keys.  (Ex.  58.)  Sound  the  tonic  chord 
first  in  all  cases.  (Cf.  Note  20.} 


Ex.  58. 


Leggiero. 

*dT 


i 


STEP  LXVil.  —  Improvise  short  melodies  in  various  minor  keys, 
closing  with  the  progression  referred  to  in  Step  LXVI.     (Ex.  59.) 


Ex.  59. 

Espressivo. 

r 

\  Jf  \¥\P  fi 

^^ 

—  N  —  rj     —  J  — 

•i  \   i          U^  * 

~^  — 

§?1*\        [r    bO 

K 

1      DT 

/htJ  •     ui  • 

51  • 

i    v^l-f              "lS 

P   -              « 

'  * 

|H 

(H/l  .       11  . 

rf  •        II 

<          *y 

r*        * 

I 

H3  HI  r 

Si 

in            II 

J  •  i  P  b  * 

•• 



• 

• 

n  *       II 

Z   b  hi  C 

• 

A 

"  b^ 

&  . 

* 

* 

*        *        *        * 

STEP  LXVin.  —  Having  played  one  octave  of  a  descending  mel- 
odic minor  scale  (Ex.  60,  A),  sound  that  form  of  the  chord  of  the 
mediant  which  is  constructed  upon  the  same  scale  (B).  Follow  the 
chord  by  suitable  harmony  and  conclude  with  the  tonic  chord  (Q. 


Plain  Harmony 


STEP  LXIX.  —  Having  played  one  octave  of  an  ascending  har- 
monic minor  scale  (Ex.  61,  .4),  sound  that  form  of  the  chord  of  the 
mediant  which  is  constructed  upon  the  same  scale  (B).  Follow  the 
chord  by  suitable  harmony  and  conclude  with  the  chord  of  the  tonic 
(C). 


B. 


1 


-z- 


Note  43.  —  //  w  important  to  remark  the  nature  of  the  difference 
between  the  two  types  of  chord  peculiar  both  to  the  supertonic  and  to  the 
mediant.  As  exemplified  in  Steps  LXIV  and  L XVII I,  these  chords 
are  concordant;  in  Steps  LXV  and  LXIX  they  are  discordant.  In 
the  latter  phase,  they  call  for  that  particular  form  of  harmonic  treatment 
known  as  resolution.  (Cf.  Note  36.)  The  most  elementary  resolution 
is,  in  both  cases,  effected  by  the  succession  of  the  chord  a  4th  above. 
Therefore,  the  student  will  do  well  to  resolve  the  supertonic  chord  with  the 
diminished  5th  upon  the  chord  of  the  dominant;  the  mediant  chord  with 
the  augmented  5th  upon  that  of  the  submediant. 


Note  44.  —  The  student  will  now  be  called  upon  to  appreciate  the 
various  mental  effects  obtained  from  one  common  chord  by  change  of 
tonal  environment.  Thus,  the  major  common  chord  in  Ex.  62,  A,  is 
that  of  the  tonic;  in  B,  that  of  the  dominant;  in  C,  that  of  the  sub- 
dominant;  in  D,  it  appears  as  the  dominant  harmony  of  a  minor  key; 
in  E,  as  that  of  the  submediant,  also  of  a  minor  key. 


Harmony  in  Pianoforte-Study 


B. 


-&- 


c. 

-7p*jf  ™  —  «•  — 

|J>      ^ 

cS 

_^  1 

-g—  « 

<5 

~0  1 

-jr 

:   ^ 

t    " 

D. 

A    u 

<5 

V  i  "                                                                                     , 

IO 

-^j 

<&* 

h^ 

J 

<5* 

(fo                                                                   <5?            «?             ^          ^ 

^ 

li 

rt 

«J                 -&           "            ^ 

/^ 

-3T3 

-^; 

u      •«- 

E. 

ntt                                                                 « 

^ 

-      J2- 

l/Jfu. 

12    <5 

%        II 

^    s 

—  ^ 

JrHi 

or—  —  :      —  ^-  —  z?  *  &!  — 

j^ 

«>         II 
-rr 

STEP  LXX.  —  Select  various  major  common  chords,  trace  them 
through  the  five  keys  in  which  they  occur  individually,  and  treat 
them  in  the  manner  exemplified  by  Ex.  62.  In  each  case  the  mental 
grasp  should  first  be  stimulated  by  playing  one  octave  of  the  scale 
concerned  or  by  sounding  the  chord  of  the  tonic. 


Note  45.  —  The  same  process  may  be  continued  in  connection  with 
minor  common  chords.  Thus,  the  chord  in  Ex.  63,  A,  is  that  of  the 
tonic;  in  B,  that  of  the  subdominant;  in  C,  it  is  transferred  to  the 
major  key  and  appears  as  the  chord  of  the  supertonic;  in  D,  as  that  of 
the  submediant;  in  E,  as  that  of  the  mediant. 


Ex.  63. 

A. 


*== 


B. 


\JjLb  -—  —  ZP      *—  1^  —  ^ 

j-tt  — 

m 

S  —  | 

L^T  23  S>  ^~ 

c. 

-z; 

--  4 
j 

& 

|o    ^ 

» 

~&  —  i 

~TL^  —                      &  —  &  —  ~  —  ~  

-»-* 

^=1 

-&- 


Plain  Harmony 


D-                                          J 

-^ 

I/    [/ 

I*J       /o 

~fir&  —                                                   ^  73  (5>  — 

-     £a 
»i     < 

^ 

\A)                                            o         <^         &                              1^1 

^ 

I 

E-                                                                                               J 

Q   k                                                                                               «<  ^ 

IO      /^i 

^ 

a 

|    ^K,b|>  .  25  S>  ^  

-    g 

a 

5?  W 

Kq?  p  «     g>  —  «  —  *"- 

^  —  : 

S  —  H 

STEP  LXXI.  —  Select  various  minor  common  chords,  trace  them 
through  the  five  keys  in  which  they  occur  individually,  and  treat 
them  in  the  manner  suggested  by  Ex.  63.  Begin,  in  each  case,  by 
playing  one  octave  of  the  scale  involved. 

Note  46.  —  It  is  impossible  to  exaggerate  the  importance  of  the 
tonal  appreciation  connected  with  Steps  LXX  and  LXXI.  The 
positive  and  negative  elements  of  tonality  —  whether  major  or  minor 
—  are  symbolized  by  the  admixture  of  major  and  minor  chords  con- 
tained within  every  form  of  key;  and  the  mental  discrimination  which 
realises  the  perpetual  presence  of  these  two  forms  of  chordal  expression 
in  music  of  every  type  is  the  gateway  to  an  understanding  of  harmony 
in  its  most  occult  forms. 


Note  47.  —  The  discords  referred  to  in  this  Part  are,  in  all  cases, 
exemplified  with  their  most  natural  form  of  resolution.  If  a  resolu- 
tion of  this  nature  were  invariably  applied  to  every  discord,  the  expres- 
sion of  harmony  would  sink  to  the  level  of  mere  conventionalism.  As 
soon  as  the  student  has  grasped  the  elements  of  the  idea  embodied  within 
the  act  of  resolution  and  has  proved  his  grasp  by  illuminative  exempli- 
fication, he  should  proceed  to  experiment  with  the  less  general,  if  less 
natural,  phases  of  resolution;  bearing  in  mind  that  the  thought  which 
underlies  the  process  is  that  of  the  absorption  of  dissonance  in  another 
harmony,  and  that,  provided  that  the  absorption  be  complete,  any  reso- 
lution of  a  discord  is  acceptable  to  the  musical  sense.  We  append  a 
few  resolutions  of  the  chord  of  the  dominant  7th.  In  Ex.  64,  A,  the 
chord  is  resolved  upon  the  harmony  of  the  submediant;  in  B,  upon  that 
of  the  subdominant;  in  C,  upon  that  of  the  super  tonic. 


Harmony  in  Pianoforte-Study 


B.     Ca 

f\     u         jf 

ntabile. 

•«•,» 

1 

* 

<•  — 

"~~N 

If    O/.  • 

• 

-*-=  

4— 

H- 

P-4- 

=r^ 

k&L&L 

f- 

rf 

^~ 

—  )*- 

-•-; 

J—  ^-h£ 

^3F 

i   r1^ 

.*£ 

F 
« 

C  1  p_ 

^f  .*-£  *^ 

—  *-^- 

».  * 

-•-              -»- 
p-T-        «± 

p      •   p'rv* 

t-V—  Kfi      | 

-J— 

tz 

•-- 

-f 

« 

»H  —  »F-- 

»-!  •    M    _    1 

^SH  ***""  ***"  ' 

^&—         ^^ 

£ 

&* 

-f  JJ  r 

i^a 

>^-U  ^ 

C.         Vivo. 

M       U                       ^-A-«- 

/fcpfe  f  *  M 

*T 

r-7 
fff* 

s 

—1  —  !  — 

-^-Tf-l 

—  « 

^  l-^^ 

•*  u*  rn 

/TN 
1  —  11_,  —  1_| 

<g>  *  "|   i    ;    !       . 

^>  £  stacc. 

rr  r  ^ 

LLi^ 

TiH*-i«-f-- 

^»  fi-^- 

**±*J 

ff    *    0    ff 

^= 

-^-l 

c   « 

r  H 

1       1   1 

1 

m    i 

*         1  1 

Jf      jl    TJ1™ 

-€—  J 

g 

, 

- 

i  . 

•   *  • 

F    ^    F    ! 

r                    1 

ICn         'I 

J_ 

5± 

|ZKjl 

z 

f-» 

—  1  —  f 

*  II 

iv|/         *r_ 

*rsr^3 

- 

-6*- 

^.7 

STEP  LXXII.  —  Improvise  progressions  in  major  and  minor  keys, 
introducing  examples  of  various  resolutions  of  the  dominant  yth:  — 
(a)  In  chordal  form;  (&)  in  decorated  form.  (Ex.  64.) 


STEP  LXXIII.  —  Combine  any  of  the  chords  —  inverted  or  un- 
inverted  —  referred  to  in  this  Part.  The  following  combinations 
should  be  regarded  merely  as  suggestive.  Each  progression  should 
be  presented  both  in  simple  chordal  form  and  in  florid  or  decorated 
form. 

(^4)   Major  Keys. 

(1)  Tonic  —  subdominant  —  dominant  (yth)  —  tonic. 

(2)  Tonic  —  mediant  —  submediant  —  dominant    (yth)  — 

tonic. 

(3)  Tonic  —  submediant  —  supertonic  —  dominant  (yth)— 

tonic. 

(4)  Tonic — dominant  —  supertonic  —  subdominant  —  domi- 

nant —  tonic. 

(B)   Minor  Keys. 

(1)  Tonic  —  subdominant  —  dominant  (yth)  —  tonic. 

(2)  Tonic  —  submediant  — -subdominant  —  tonic. 

(3)  Tonic  —  submediant  —  harmonic    supertonic  —  domi- 

nant (yth)  —  tonic. 

(4)  Tonic  —  dominant  —  harmonic  mediant  —  submediant 

—  subdominant  —  tonic. 

End  of  Part  I. 


PART    II 

Auxiliary   Sounds 

Note  48.  —  Music  is  composed  of  two  species  of  sounds:  —  (a) 
Those  which  form  a  part  of  the  prevailing  chord  or  harmony,  (b)  those 
which  are  foreign  to  the  harmony.  All  the  sounds  referred  to  or  de- 
scribed in  Part  I  are  of  the  former  species;  those  indicated  by  asterisks 
in  Ex.  65  belong  to  the  latter. 


Ex.  65. 


^-J±$tl  —  ,5)  

—x— 

-0  ^— 

in  —  =«:  —  «  

—  r 

Fed. 


*     Fed. 


*     Fed. 


Note  49.  —  An  introductory  experiment  is  necessary  to  explain  the 
operation  and  nature  of  auxiliary  sounds.  A  series  of  repeated  sounds 
may  be  played  during  the  continuance  of  a  chord  of  which  the  repeated 
sounds  do  not  form  a  part.  (Ex.  66,  A.)  No  explanation  will  be 
necessary  to  indicate  the  unmusical  character  of  the  effect  produced. 
If,  however,  the  same  sounds  are  followed  immediately  by  sounds  of  the 
harmony  (IS),  the  process  satisfies  the  musical  sense.  This  process  is 
analogous  to  the  act  of  resolution  referred  to  in  Note  36. 


34  Harmony  in  Pianoforte-Study 

'  —     _^__^ 

_»_~__     ____»^_»  «.  i 

,  j. j. . j. j. j. j. v -j^J    ±5±*±5^?^i 


STEP  LXXEV.  —  Play  examples  oi  single  major  and  minor  com- 
mon chords.  In  each  case,  introduce  auxiliary  sounds  as  in  Ex.  66, 
B,  repeating  them  several  times  before  the  act  of  resolution. 

N.  B.  —  Each  auxiliary  must  be  one  scale-degree  above  any  one 
sound  of  the  chord  selected. 


Note  50.  —  An  auxiliary  sound  stands  in  the  place  of  the  harmonic 
sound  which  it  displaces  temporarily.  The  characteristic  dissonance 
of  such  a  sound  arises  from  the  fact  that  the  sound  of  resolution  is 
mentally  inferred  at  the  moment  when  the  auxiliary  is  heard.  Hence, 
the  sounds  indicated  by  asterisks  in  Ex.  67,  A ,  are  not  auxiliary  sounds, 
because  the  ear  expects  them  to  be  followed  by  the  harmonic  sounds 
which  they  have  displaced.  In  B,  on  the  contrary,  the  sounds  similarly 
marked  are  in  each  case  resolved  upon  the  neighboring  harmonic  sounds, 
and  the  ear  is  satisfied. 


Ex.  67. 


B. 


^=^^ 


STEP  LXXV.  —  With  the  left  hand  play  the  tonic  chord  of  any 
major  key;  with  the  right  hand  play  successively: — (a)  A  sound 
of  the  harmony,  (6)  an  auxiliary  sound  one  scale-degree  above,  (c) 
the  original  harmonic  sound.  Repeat  in  various  major  keys.  The 
process  is  illustrated  by  Ex.  68,  and  may  be  adapted  to  different 
times  and  figurations. 


Ex.  68. 


Auxiliary  Sounds 


35 


Step  LXXVI.  —  Proceed  as  in  Step  LXXV,  playing  the  moving 
part  below  the  chord.     (Ex.  69.) 


Ex.  69. 


CD"  fi  —  S^T— 

55  "  -  -  - 

V     "  —  <£.'•*                         •• 

-C*T  ' 

-f~*  —  ^  —  *  —     —  J  r~ 

~i  H 

^T-bH—                         ^  —  »—  ,— 

^  ••  '  J  r  J  r 

•1        "*       1  1 

s  —  H 

****** 


STEP  LXXVH.  —  Transfer  Steps  LXXV  and  LXXVI  to  minor 
keys. 


Note  51.  —  Auxiliary  sounds  may  consist  of  the  scale-degree  of  the 
prevailing  key  or  of  sounds  which  belong  specifically  to  the  chromatic 
scale  of  the  same  key.  Those  treated  hitherto  are  of  the  former  kind; 
those  now  to  be  considered  include  the  latter. 

STEP  LXXVIH.  —  With  the  left  hand,  play  the  tonic  chord  of 
any  major  key;  with  the  right  hand,  play  in  succession:  —  (a)  A 
sound  of  the  harmony,  (6)  an  auxiliary  sound  one  semitone  below, 
(c)  the  original  harmonic  sound.  (Ex.  70.)  Repeat  in  several  major 
keys,  employing  various  time-groupings  and  figurations. 

Ex.  7O. 


(4^f 

PS  — 

s  — 

V 

-ihid  —  j"  r  r  —  r- 

H 

•*• 

5             •*»- 

g"V'^ 

f^ 

-P  5S  

^      ii 

5  ^ 

^% 

r 

^      II 

* 

1  —  1  1  —  II 
***** 

STEP  LXXIX.  —  Proceed  as  in  Step  LXXVIII,  playing  the  mov- 
ing part  below  the  chord.     (Ex.  71.) 


Ex.  71. 


Sfi: 


36  Harmony  in  Pianoforte-Study 

STEP  LXXX.  —  Transfer  Steps  LXXVIII  and  LXXIX  to  minor 

keys. 

****** 

Note  52.  —  The  auxiliary  sounds  considered  hitherto  have  been  cen- 
tred round  the  individual  members  of  a  single  chord.  No  provision 
has  yet  been  made  for  progressing  from  one  sound  of  a  chord  to  another. 
In  a  broad  sense,  this  may  be  illustrated  by  a  passage  passing  through 
every  sound  of  the  scale  during  the  prevalence  of  the  tonic  harmony. 
(Ex.  72.) 

Ex.  72.         


I 


STEP  LXXXI.  —  Play  scale-passages   above  or  below  the  tonic 
harmony  of  various  major  keys  after  the  manner  of  Ex.  73. 

Ex.  73. 


1 


^     \\A 


STEP  LXXXIL  —  Transfer  Step  LXXXI  to  minor  keys,  using  (a) 
the  harmonic  scale,  (b)  the  melodic  scale. 


STEP  LXXXIQ.  —  Introduce  diatonic  auxiliary  sounds  between 
the  various  members  of  major  common  chords.  This  should  be 
done  in  various  times,  with  diverse  figurations  and  at  various  oc- 
taves. It  will  be  noted  (Ex.  74)  that  a  single  auxiliary  suffices  be- 
tween the  root  and  3rd  or  between  the  3rd  and  5th;  while,  between 
the  5th  and  octave,  two  such  sounds  are  necessary. 


Ex.  74. 


Auxiliary  Sounds 


37 


STEP  LXXXIV.  —  Proceed  as  in  Step   LXXXIII,  playing   the 
moving  part  below  the  chord.     (Cf.  Exs.  69  and  71.) 


STEP  LXXXV.  —  Transfer  Steps  LXXXIII  and  LXXXIV  to 
minor  keys,  using  (a)  the  harmonic  scale,  (6)  the  melodic  scale. 
(Ex.  75-) 

Ex,  75. 

Moderate. 


Note  53.  —  TTie  use  o/  the  melodic  minor  scale  enjoined  here  will 
demonstrate  the  origin  of  the  name  and  the  purpose  of  the  scale  in  the 
most  effective  manner.  Speaking  broadly,  the  major  6th  and  major 
?th  are  employed  in  ascending  passages,  the  minor  6th  and  minor  ?th 
in  those  which  move  downwards. 


STEP  LXXXVI.  —  Introduce  chromatic  auxiliary  sounds  between 
the  various  sounds  of  major  common  chords.  As  before,  different 
times  and  figurations  should  be  attempted.  Ex.  76  is  a  chromatic 
version  of  Ex.  74. 


Ex.  76. 


38  Harmony  in  Pianoforte-Study 

STEP  LXXXvlI.  —  Proceed  as  in  Step  LXXXVI,  playing  the 
moving  part  below  the  chord. 


STEP  LXXXVni.— Transfer  Steps  LXXXVI  and  LXXXVII  to 
minor  keys.     Ex.  77  is  a  chromatic  version  of  Ex.  75. 

Ex.  77. 

Moderate. 


Note  54.  —  The  student  has  now  demonstrated  his  power  to  form  an 
independent  melody  upon  one  harmony.  It  is  extremely  rare,  however, 
to  find  a  melody  constructed  upon  so  limited  a  basis.  Variety  in 
melodic  formation  calls  for  the  use  of  many  harmonies,  and  the  facility 
with  which  an  auxiliary  sound  joins  two  members  of  the  same  chord  is 
but  a  faint  indication  of  its  power  to  connect  sounds  belonging  to  differ- 
ent harmonies.  The  continuity  of  the  melody  of  Ex.  78  is  the  outcome 
of  the  use  of  the  auxiliary  sounds  indicated  by  the  asterisks. 

Ex.  78. 

Andante. 


Fed. 


Auxiliary  Sounds 


39 


Fed. 


STEP  LXXXIX.  —  Combine  the  dominant  and  tonic  chords  in 
various  major  keys.  Add  a  diatonic  melody,  using  auxiliary  sounds 
in  the  process.  (Ex.  79.)  Sound  the  tonic  harmony  before  each 
example.  (Cf.  Note  20.) 

Ex.  79. 


i 


STEP  XC.  —  Transfer  Step  LXXXIX  to  minor  keys. 


STEP  XCI.  —  Repeat  Steps  LXXXIX  and  XC,  employing  oc- 
casional chromatic  auxiliary  sounds.  Ex.  80  is  a  chromatic  version 
of  Ex.  79. 

Ex.  8O. 


4o 


Harmony  in  Pianoforte-Study 


STEP  XCII.  —  Combine  the  chords  of  the  subdominant,  dominant 
and  tonic  in  various  major  keys.  Add  a  diatonic  melody,  employing 
auxiliary  sounds  in  the  process.  Sound  the  tonic  harmony  before 
playing  each  example.  (Cf.  Note  20.) 

******. 

STEP  XCIII.  —  Transfer  Step  XCII  to  minor  keys.     (Ex.  81.) 

Ex.  81. 


STEP  XCIV.  —  Repeat  Steps  XCII  and  XCIII,  employing  oc- 
casional chromatic  auxiliary  sounds.  Ex.  82  is  a  chromatic  version 
of  Ex.  81. 


Ex.  82. 


-= • •  n'lLal ^1^      ~l 

3       b!       g    j        !        |    => 


fe 


****** 


Auxiliary  Sounds 


Note  55.  —  //  is  an  essential  characteristic  of  all  auxiliary  sounds 
that  they  should  proceed  to  their  sounds  of  resolution  by  the  step  of  a 
second;  but  it  is  not  necessary  that  they  should  be  approached  in  the 
same  manner.  Any  auxiliary  sound  may  be  approached  by  leap. 
The  auxiliaries  in  Ex.  83  are  thus  treated  in  every  instance. 


Ex.  83. 

Moderate. 


Fed. 


STEP  XCV.  —  Add  to  various  tonic  chords,  major  and  minor, 
melodic  passages  containing  diatonic  auxiliary  sounds  approached 
by  leap.  (Ex.  84.) 


Ex.  84. 

Teneramente. 


W^ 

1         >•              «H       ^              «•]     Bi 

=^  —  ^H  —  Jn 

f\  •   ^    K   - 

jj     X        i    X        ^..[j» 

-^r-^-ld 

9 

H:  J— 

rinf. 


STEP  XCVI.  —  Form,  upon  the  following  harmonic  bases,  melo- 
dies containing  diatonic  auxiliary  sounds  approached  by  leap. 

(A)  Major  Keys. 

(1)  Tonic,  dominant,  tonic. 

(2)  Tonic,  subdominant,  dominant,  tonic. 

(3)  Tonic,  submediant,  supertonic,  dominant,  tonic. 


i  Harmony  in  Pianoforte-Study 

(B)  Minor  Keys. 

(1)  Tonic,  dominant,  tonic. 

(2)  Tonic,  subdominant,  dominant,  tonic. 

(3)  Tonic,  subdominant,  submediant,  dominant,  tonic. 


STEP  XCVII.  —  Add  to  various  tonic  chords,  major  and  minor, 
melodic  passages  containing  chromatic  auxiliary  sounds  approached 
by  leap. 

Note  56.  —  The  direction  to  add  chromatic  auxiliary  sounds  must 
not  be  interpreted  as  meaning  that  every  sound  of  the  kind  is  to  be  chro- 
matic. Ex.  85  is  a  chromatic  version  of  Ex.  83;  and  the  student  will 
remark  that  auxiliary  sounds  of  both  types,  diatonic  and  chromatic, 
are  included. 

Ex.  85. 

Moderate. 


Fed.      * 


STEP  XCVin.  —  Form,  upon  the  harmonic  bases  given  in  Step 
XCVI,  melodies  containing  chromatic  auxiliary  sounds  approached 
by  leap. 


Note  57.  —  Auxiliary  sounds  may  occur  upon  a  non-accented  beat 
or  upon  the  weaker  part  of  an  accented  beat;  or  they  may  be  introduced 
upon  an  accented  beat  or  upon  the  stronger  part  of  any  beat,  accented  or 
unaccented.  The  appoggiatura  furnishes  a  familiar  example  of  the 
latter  kind.  The  auxiliaries  treated  hitherto  fall  upon  the  weaker 
parts  of  the  bars  or  beats;  in  Ex.  86  they  occur  throughout  upon  the 
stronger. 

Ex.  86. 

Allegretto. 


Auxiliary  Sounds 


43 


STEP  XCIX.  —  With  the  left  hand,  play  the  tonic  chord  of  any 
major  key  and  in  any  position  or  inversion;  with  the  right  hand, 
add  a  melody  containing  accented  diatonic  auxiliary  sounds  after 
the  manner  of  Ex.  86. 


STEP  C.  —  Proceed  as  in  Step  XCIX,  playing  the  moving  part 
in  the  bass.     (Ex.  87.) 

Ex.  87. 

Allegrttto. 


STEP  CI.  —  Transfer  Steps  XCIX  and  C  to  minor  keys.    (Ex.  87.) 
****** 

STEP  OH.  —  Proceed  as  in  Steps  XCIX  and  C,  playing  each  auxil- 
iary sound  at  the  distance  of  a  semitone  below  the  harmonic  sound. 
This  will  entail  the  use  of  chromatic  auxiliary  sounds.  (Ex.  88.) 

Ex.  88. 

Esfressivo. 


STEP  Cffl.  —  Transfer  Step  CII  to  minor  keys. 
****** 


44 


Harmony  in  Pianoforte-Study 


STEP  CIV. — Form,  upon  the  harmonic  bases  given  in  Step  XCVI, 
melodies  containing  examples  of  diatonic  accented  auxiliary  sounds. 
(Ex.  89.) 


Ex.  89. 

Generoso. 


STEP  CV.  —  Proceed  as  in  Step  CIV;    but  introduce  auxiliary 
sounds  of  both  types,  diatonic  and  chromatic. 


Note  58.  —  One  of  the  most  striking  evidences  of  the  value  of  the 
auxiliary  sound  in  respect  to  musical  effect  is  obtained  by  sounding  the 
auxiliary  together  with  the  chord  upon  which  it  is  superimposed;  and, 
it  may  be  added,  no  slight  difficulty  is  often  experienced  by  the  student 
who,  in  such  cases,  is  inclined  to  confuse  the  foreign  sounds  with  those 
belonging  to  the  prevailing  harmony.  The  auxiliary  sounds  in  Ex. 
90  are  all  easily  recognisable  as  such,  but  the  charm  which  accompanies 
their  dissonance  against  the  respective  chords  may  not  be  immediately 
perceptible.  The  harmonic  education  of  the  ear  is  rarely  of  greater 
importance  than  in  this  particular  phase  of  aural  appreciation. 

Ex.  9O.  

Sonore.  ^- 


* 


cresc. 


r/'T  —  »— 

& 

-\        — 

\    ^     \ 

— 

—  ~^\  

3  3  

1 

-& 

**        -&       •& 

#£- 


1 


Auxiliary  Sounds 


45 


STEP  CVI.  —  Incorporate  auxiliary  sounds,  diatonic  or  chromatic, 
with  the  members  of  the  tonic  harmony  in  various  keys,  major  and 
minor:  (a)  In  plain  form  (Ex.  91,  .4);  (6)  in  decorated  form  (B).* 


Ex.  9  1  . 


4 


J 


i 


B.    Grazioso. 


STEP  CVII.  —  Proceed  as  in  Step  CVI,  taking  the  dominant  and 
tonic  chords  as  the  basic  harmony.     (Ex.  92.) 


Ex.  92. 

Grazioso. 


•  This  may  appear  to  be  an  unnecessary  repetition  of  Steps  XCIX,  etc.  It  must  be  ob- 
served, however,  that  the  attention  of  the  student  is  here  directed  to  the  chordal  aspect  of  the 
auxiliary  sound  as  compared  with  that  phase  of  the  sound  which  is  more  particularly  concerned 
with  pairing  from  one  melodic  sound  to  another. 


46 


Harmony  in  Pianoforte-Study 


STEP  CVin.  —  Improvise  phrases  containing  chords  treated  as  in 
Ex.  90.  The  harmonic  bases  given  in  Step  XCVI  may  be  regarded 
as  suggestive. 


Note  59.  —  The  law  which  directs  the  resolution  of  an  auxiliary 
sound  by  the  step  of  a  2nd  is  apparently  broken  in  Ex.  pj.  This,  how- 
ever, is  not  the  case.  The  auxiliary  sounds  above  and  below  the  har- 

Ex.  93. 


manic  sounds  A  and  F  are  both  brought  into  play  and  the  resolution  is 
therefore  only  postponed.  This  most  useful  device  is  known  as  a 
11  changing-note"  and  the  term  implies  the  obvious  changing  of  one 
auxiliary  for  another.  One  of  the  most  familiar  examples  of  the  use 
of  changing-notes  may  be  found  in  the  first  subject  of  Weber's  "Rondo 
Brillante  "  in  E  flat,  of  which  we  quote  the  first  bars.  (Ex.  94.} 

Ex.  94. 

Moderate  e  con  grazia. 


B:.b2a     A 
^  9  b4  H    I  E 


E 


STEP  CIX.  —  Form  changing-notes  upon  various  chords,  major 
and  minor;  or  upon  various  combinations  of  chords.     (Ex.  95.) 


Auxiliary  Sounds 


47 


Ex.  05. 

Allegro. 


Note  60.  —  We  have  seen  that  the  use  of  auxiliary  sounds  below  the 
members  of  a  chord  entails  the  introduction  of  chromatic  sounds  on 
those  foreign  to  the  key-signature.  Sounds  of  this  nature  may  be  freely 
employed  in  passing  from  chord  to  chord,  provided  that  the  one  con- 
dition common  to  the  use  of  all  auxiliary  sounds  be  observed  —  that 
resolution  be  effected  strictly  by  conjunct  means  or,  in  other  words,  by 
the  step  of  a  2nd.  (Cf.  Note  55.)  Ex.  96  contains  sounds  of  this  kind. 


Ex.  96. 


i 


Note  61.  —  rAe  student  is  now  in  a  position  to  improvise  progres- 
sions formed  upon  the  tonal  harmonies  generally,  and  it  should  be  his 
ambition  steadily  to  increase  the  number  of  chords  used.  The  chordal 


48  Harmony  in  Pianoforte-Study 

successions  outlined  in  Step  XCVI  have  been  frequently  used  as  ex- 
amples of  basic  harmonies,  and  they  possess,  at  least,  the  merits  of 
simplicity  and  directness.  But  the  student  must  no  longer  be  content 
to  limit  his  exemplification  to  harmonic  conventions;  on  the  contrary,  he 
must  begin  to  experiment  in  the  broadest  possible  manner.  The  com- 
binations opened  up  by  the  accented  auxiliary  sound  are  practically 
inexhaustible;  and,  at  the  present  stage,  there  is  no  better  way  of  cul- 
tivating aural  discernment  and  facility  in  musical  self-expression. 

End  of  Part  H. 


PART    III 

Cadences 

Note  62.  —  Before  proceeding  to  the  substance  of  this  Part,  the 
student  is  counselled  to  make  a  careful  examination  of  Lussy-Dutoit' s 
"  Short  Treatise  on  Musical  Rhythm.11*  It  is  impossible  to  progress 
to  any  extent  in  harmonic  facility  until  the  connection  between  harmony 
and  the  musical  cadence,  as  the  defining  medium  of  rhythm,  is  per- 
fectly clear  to  the  musical  sense. 

Note  63.  —  In  musical  parlance  and  regarded  broadly  the  cadence  is 
the  close  of  a  musical  thought.  The  following  thoughts  from  Beethoven's 
Sonatas  may  be  played  at  this  point  to  illustrate  the  function  of  the 
final  cadence,  the  attention  being  confined  in  each  case  to  the  effect  of 
the  last  two  harmonies: 

Op.  2,  No.  i:  second  mov.,  bars  23  to  27. 
Op.  2,  No.  3:  first  mov.,  bars  Q  to  ij. 
Op.  2,  No.  3:  third  mov.,  bars  8  to  16. 
Op.  7:  fourth  mov.,  bars  I  to  8. 
Op.  10,  No.  2:  second  mov.,  bars  i  to  8. 
Op.  14,  No.  i:  third  mov.,  bars  i  to  8. 

Note  64.  —  Two  chordal  combinations  of  a  cadential  nature  were 
referred  to  in  the  course  of  Part  I  (Steps  XV,  XX,  XXV,  XXX). 
Since  these  are  generally  used  at  the  close  of  musical  thoughts,  they 
form  examples  of  the  final  cadence  or  the  full  stop  of  the  musical  lan- 
guage. 

Note  65.  —  Scarcely  less  important  than  the  cadence  itself  is  the 
harmony  by  which  it  is  approached.  The  many  Steps  of  Part  I  which 
call  for  the  combination  of  three  chords  will  have  prepared  the  student 
to  approach  the  dominant  harmony  in  various  effective  ways;  but  since 
it  is  not  possible  to  conceive  a  cadence  in  the  absence  of  an  idea  to  be 
cadenced,  he  should  strive  to  gain  the  utmost  facility  in  the  expression 
of  the  harmonies  which  form  the  main  part  of  each  thought.  The  tran- 
sition to  the  closing  harmonies  will  then  be  natural  and  free  from  arti- 
ficiality. The  elementary  combinations  suggested  in  Step  XCVI  may 
first  be  used  as  basic  models  for  the  expression  of  properly  cadenced 
progressions. 

*  English  translation  by  the  author  (Winthrop  Rogers,  Ltd.). 

49 


5©  Harmony  in  Pianoforte-Study 

STEP  CX.  —  Improvise  short  harmonic  progressions  in  various 
major  keys,  ending  with  a  full  close  in  the  tonic.  Place  the  3rd 
in  the  uppermost  part  of  the  penultimate  or  dominant  chord,  so 
that  it  may  proceed  naturally  to  the  octave  of  the  tonic  in  the  final 
chord. 


STEP  CXI.  —  Transfer  Step  CX  to  minor  keys. 


Note  66.  —  A  perfect  cadence  is  often  presented  in  such  a  manner 
that  the  effect  of  finality  is  modified  considerably.  Thus,  the  tonic  chord 
may  contain  the  jrd  or  $th  in  the  top  part;  in  either  case,  the  final  force 
will  be  greatly  lessened.  In  Ex.  97  both  types  are  illustrated;  the 
cadence  at  *  is  but  semi-final;  that  at  **  is  absolute. 


Ex.  97. 


BEETHOVEN.     Sonata,  Op.  90. 


[/•**,, 

8*9       1 

m            w              ^ 

H           y 

~           * 

"«* 

1 

1 

-* 

-» 

I 


.•    ,•    r  ^  * 


f     •     M     * 


P  f  P  f 


i^TTfr 
*     •+  3  \ 


4 


Cadences  $  i 

STEP  CXII.  —  Improvise  short  harmonic  progressions  in  various 
major  keys,  ending,  in  each  case,  with  a  perfect  cadence  in  the  tonic 
of  the  non-absolute  type. 


STEP  CXm.  —  Transfer  Step  CXII  to  minor  keys. 

****** 

Note  67.  —  Like  their  prototypes,  the  stop-points  of  literature,  the 
cadences  of  music  are  definitely  final,  semi-final,  or  distinctly  non- 
final;  further,  an  infinity  of  shade  significances  lie  between  the  ex- 
tremes of  absolute  finality  and  absolute  non-finality.  Thus,  the  semi- 
finality  of  the  dominant-tonic  cadence  just  illustrated  may,  as  in  Ex. 
Q8,  be  made  still  less  final  by  the  use  of  inversions. 

Ex.  98. 

Maestoso. 


i 


j=£i 


. 

</***. 


I 


? 


i 


STEP  CXIV.  —  Improvise,  in  various  major  keys,  short  progres- 
sions ending  with  the  dominant-tonic  cadence,  one  chord  or  both 
chords  being  in  inverted  form. 

N.B.  —  The  last  inversion  of  the  dominant  yth  (Step  LIII)  may 
be  used  most  aptly  for  this  purpose. 


STEP  CXV.  —  Transfer  Step  CXIV  to  minor  keys. 

****** 

STEP  CXVI.  —  Improvise,  in  various  major  keys,  short  rhythmic 
progressions;  ending,  in  each  case,  with  the  subdominant- tonic 
cadence,  both  chords  being  in  the  root-position.  (Ex.  99.)  (Cf. 
Step  XXV.) 

Ex.  99. 


'dncio .  ~.     '      ^ 

;j?j  ffi 

-* — -3   x  r    -F 


dim. 


lal 


s->r     x  l  **=>, 


Harmony  in  Pianoforte-Study 


Note  68.  —  This  cadence  is  comparatively  seldom  used  to  indicate 
finality  in  instrumental  music,  but  it  is  of  frequent  occurrence  in  choral 
and  particularly  in  church  music.  The  student  should,  however,  be 
familiar  with  its  use  at  the  keyboard. 


STEP  CXVH.  —  Transfer  Step  CXVI  to  minor  keys. 


STEP  C  XVIII.  —  Proceed  as  in  Step  CXVI,  but  present  each  ca- 
dence in  inverted  form. 


Ex.  1OO. 

Deciso. 


STEP  CXIX.  —  Transfer  Step  CXVI  1 1  to  minor  keys.     (Ex.  IOO.) 


Note  69.  —  Many  varieties  exist  of  the  cadence  used  to  produce  an 
effect  of  non-finality,  of  incompleteness  and  abeyance  of  idea.  The 
most  usual  form  is  that  in  which  the  harmony  of  the  dominant  is  the 
last  heard.  (Ex.  101.) 


Cadences 


53 


Ex.  101. 
Allegro  vivace. 


BEETHOVEN.    Sonata,  Op.  31,  N<x  i. 


Note  70.  —  In  a  non-final  cadence,  any  harmony  may  precede  that 
of  the  dominant. 

STEP  CXX.  —  Improvise  short  progressions  in  various  major  keys; 
ending,  in  every  case,  upon  the  harmony  of  the  dominant. 


STEP  CXXI.  —  Transfer  Step  CXX  to  minor  keys. 


Note  71.  —  A  very  general  form  of  the  non-final  cadence  consists  of 
the  second  inversion  of  the  tonic  harmony  and  the  root-position  of  the 
dominant,  both  formed  upon  the  same  bass  sound.  (Ex.  102.) 


Ex.  1O2. 

Tempo  di  Menuetto. 


BEETHOVEN.     Sonata,  Op.  49,  No.  2. 


"  1 


STEP   CXXII.  —  Improvise   short  progressions  in  various  major 
keys;  ending,  in  every  case,  with  the  cadence  described  in  Note  71. 


STEP  C XXIII.  —  Transfer  Step  CXXII  to  minor  keys. 


Note  72.  —  A  phrase  or  progression  which  ends  upon  the  tonic  har- 
mony produces  an  effect  of  completeness;  ended  upon  the  harmony  of 
the  dominant,  the  effect  is  one  of  incompleteness,  of  thought-suspension. 
Hence  it  follows  that  when  a  melody  or  musical  thought  consists  of  two 
phrases,  the  first  is  usually  terminated  by  an  incomplete  or  dominant 
cadence,  the  second  by  a  complete  or  tonic  cadence.  (Ex.  103.) 


$4  Harmony  in  Pianoforte-Study 

Ex.  1O3. 


Largo  appassionato. 


BEETHOVEN.    Sonata,  Op.  2,  No.  2. 


i 


M 


?=* 


i 


f-frt 


i 


^ff^rfrffr^ 


STEP  CXXTV.  —  Improvise  two  phrases,  the  second  being  of  the 
nature  of  a  response  to  the  first;  the  first  phrase  to  end  upon  the 
dominant  harmony,  the  second  upon  that  of  the  tonic. 


STEP  CXXV.  —  Transfer  Step  CXXIV  to  minor  keys. 


Note  73.  —  An  effect  of  great  harmonic  significance  is  often  pro- 
duced by  the  skilful  avoidance  of  a  direct  cadence.  The  penultimate 
sound  in  the  melody  of  Ex.  104  is  accompanied  by  the  dominant 
harmony,  and  the  trained  musical  sense  will  expect  the  tonic  harmony 
to  follow.  The  chord  of  the  submediant  is,  however,  substituted,  the 
cadence  natural  to  the  passage  being,  as  it  were,  thwarted  or  left  in  the 
lurch. 


Cadences 


5  5 


Ex.  1  04. 

Allegro 


BEETHOVEN.    Sonata,  Op.  10,  No.  3. 


m 


STEP  CXXVI.  —  Improvise  single  phrases  in  various  major  keys. 
The  penultimate  sound  of  each  melody  must  be  accompanied  by 
the  dominant  harmony,  the  latter  being  followed  unexpectedly  by 
the  submediant  chord  in  place  of  that  of  the  tonic. 


STEP  CXXVH.  —  Transfer  Step  CXXVI  to  minor  keys. 

Note  74.  —  The  difference  of  effect  between  the  two  phases  of  the 
submediant  harmony  used  in  this  manner  is  most  marked.  The  sub- 
mediant  chord  of  the  major  key  is  minor  (cf.  Ex.  38);  in  the  minor 
key  the  same  chord  is  major  (cf.  Ex.  54).  Moreover,  the  movement 
of  the  bass  part  varies  with  the  mode.  In  the  major  key  the  bass  pro- 
gresses a  whole  tone  from  the  5th  to  the  6th  degree;  in  the  minor  the 
movement  is  but  a  semitone.  It  is  the  natural  result  of  these  differences 
to  bestow  upon  the  interrupted  cadence  in  the  minor  mode  an  effect  of 
greater  unexpectedness  and,  relatively,  of  greater  brilliance. 


STEP  CXXVin.  —  Improvise  musical  thoughts  consisting  of  two 
phrases  in  various  major  keys;  the  first  phrase  to  end  with  the  in- 
terruption of  a  cadence,  the  second  with  a  full  close  in  the  key  of  the 
tonic. 


STEP  C XXIX.  —Transfer  Step  CXXVIII  to  minor  keys. 


Note  75.  —  //  has  been  said  ( Note  69}  that  there  are  many  varieties 
of  the  non-final  cadence;  but  it  must  not  be  imagined  that  these  varieties 
are  concerned  solely  with  modifications  or  inversions  of  the  cadences 
already  discussed.  It  is  perhaps  not  an  exaggeration  to  state  that 
any  harmony  may  be  employed  as  the  final  unit  at  the  close  of  an  in- 
termediate progression.  The  two  rhythmic  fragments  of  Ex.  105,  from 
a  musical  thought  by  Beethoven,  exhibit  a  cadence  upon  the  subdomi- 
nant  twice  repeated  in  different  keys. 


Harmony  in  Pianoforte-Study 

Ex.  1  O5.  Sonata,  Op.  7,  1st  may. 


1 


-=1 Jr 


it 


STEP  CXXX.  —  The  student  is  now  advised  to  experiment  with 
non-final  cadences  of  various  types.  To  do  this  effectively,  he  must 
recall  the  necessity  for  a  true  rhythmic  presentation  in  the  expres- 
sion of  the  briefest  musical  thought.  Hence,  he  may  take  the  first 
progression  of  Ex.  105  as  a  model  for  his  first  efforts.  Every  chord 
treated  in  Part  I  should  be  tested  with  regard  to  its  cadential  possi- 
bilities, the  aim  being  the  creation  of  brief,  simple,  and  necessarily 
incomplete  progressions  distinguished  by  wide  diversity  in  their 
closing  harmonies.  The  major  and  minor  modes  should  be  used 
alternately.  The  following  is  an  example. 


Ex.  106. 

Espressivo, 


m 


i     i 

*F^E^ 
=fe  3E 


Note  76.  —  The  student  may  with  profit  complete  such  a  progression 
by  adding  another  which  closes  with  a  perfect  cadence.  Thus,  Ex.  107 
may  be  regarded  as  the  completion  of  Ex.  106. 


Ex.  1O7. 


Cadences 


57 


STEP  CXXXI.  —  Improvise  musical  thoughts  of  three  phrases  in 
various  keys,  major  and  minor;  the  first  phrase  to  end  with  a  domi- 
nant cadence  or  half-close;  the  second,  with  an  interrupted  cadence; 
the  third,  with  a  full  close  on  the  tonic.  (Ex.  108.) 


Ex. 

A 

1O8. 
Allegretto. 

r                   i         ^          -  —  i  — 

XK  bfj 

3  —  H  I  —  E3E: 

_^        _^_        ~^- 

<SF4- 

~.        -*-•  —  •   ' 

N.                   S.                   §                    <2.                                             P     . 

1 

>r      t  *  *  "  '    •      r; 

1                                                            .  ««/• 

*¥-& 

j;      i  C    x  —  x—  I 

~x  —  x  —  j  —  ^J  —  3  —  =r:  

.. 

—  &^j  P  —  ^  —  =i  — 

—  3  (5*  ^  1  ^~ 

i  —  J-^—  -J  —  ^-i  —  i  ri  ii 

m^ 

1-  ^   J    If  8  |b   *" 
1 

—  *  —  0  —  •*  1  —  1  —  i  —  i-i 

-&T—    T~x  Tl  •    '-^i.'11 

frw^r.  <//»*. 

Jt *    -^ 


1 


^ 


STEP  CXXXII.  —  Improvise  musical  thoughts  of  four  rhythmic 
periods  in  various  keys,  major  and  minor.  The  cadences  may  be 
arranged  at  the  will  of  the  player,  with  the  exception  of  the  final 
cadence,  which  must  be  a  full  close  on  the  tonic.  (Ex.  109.) 

Ex.  1O9. 
Allegretto. 


End  of  Part 


PART    IV 

Chordal   Transference 

Note  77.  —  Chords  are  linked  together  by  two  distinct  forces:  — 
(a)  By  the  presence  of  tonality  or  key;  (b)  by  affinities  existing  between 
chord  and  chord  without  direct  reference  to  key.  The  simplest  ex- 
ample of  pure  chordal  affinity  may  be  observed  in  two  chords  linked  by 
one  sound  which  they  possess  in  common.  (Ex.  no.) 

Ex.  1  10. 


STEP  C XXXIII.  —  Having  played  any  major  common  chord,  fol- 
low it  by  another  chord  linked  to  the  first  by  a  common  sound. 
A  large  number  of  examples  may  be  obtained.  In  Ex.  in,  A,  the 
original  root  becomes  the  3rd  of  another  major  common  chord; 
in  B,  the  same  sound  becomes  the  5th.  In  C  and  D,  the  original 
3rd  becomes  the  root  and  5th  respectively;  while  in  E,  the  root  of 
the  second  chord  springs  from  the  5th  of  the  original  chord.  F  to 
L  illustrate  the  same  process  in  proceeding  to  a  minor  common  chord 
under  like  conditions. 


F. 


-2?- 

C*  -fr- 

G.  H.  I.  J.  K.   . ,      L. 


Jl'  -19-       -19-        1L  ' 

-4&s> — | r-y9 — z&9 — n 

~»>      ^~* — ^s^cfe-wfa--^ 

Cug — |~U^ g —      g*    ^J> 

^g=Rg=j.    '     ^      fe~U 


STEP  C XXXIV.  —  Apply  simple  forms  of  decoration  to  the  pro- 
gressions of  the  previous  Step.  Three  phases  of  embellishment 
should  be  attempted:  —  (a)  With  plain  chordal  or  arpeggio  treat- 
ment (Ex.  112);  (6)  with  unaccented  auxiliary  sounds  (Ex.  113); 
(c)  with  accented  auxiliary  sounds  (Ex.  114). 

58 


Chordal  Transference 


59 


Ex.  1  12. 


n»  f    ff    |fp    'f    fan.  rfTt^Jt^llb^-H 

^S  ^  ^  ^5  ^rfT^:faca±dgl: 


S5 


^ 


i 


M^ 


Ex.  1  13. 

Volante 


Ex.  1  14. 

y?  ndante. 


0             I™""" 

^  ^ 

—  i  i  H 

i  —  fe- 

3-| 

/ffci  •»  —  ^—  fc 

1  —  *  

—  '-H 

1  1  " 

-fri 

i  — 

^   i 

P 

m  *   t 

__^- 

_^ 

"*f 

4 

J  

4- 

—  i 

i  — 

• 

#***** 


6o 


Harmony  in  Pianoforte-Study 


STEP  CXXXV.  —  Proceed  as  in  Step  CXXXIII,  taking  any  minor 
common  chord  as  the  antecedent  harmony.  A  few  examples  are 
appended. 


C. 


D. 


E. 

-19- 


l~  I    g»      fry 
I    g    V' 


STEP  CXXXVI.  —  Apply  forms  of  embellishment  to  the  progres- 
sions of  Step  CXXXV,  after  the  manner  of  Exs.  112,  113  and  114. 


Note  78.  —  Three  chords,  all  having  one  sound  in  common,  may  now 
be  linked  together;  but,  as  heretofore,  without  reference  to  key.  In  Ex. 
116  the  common  sound  proceeds  from  the  5th  of  the  antecedent  chord; 
in  Ex.  117,  from  the  root. 


Ex.  1  16. 


Ex.  1  17. 


STEP  CXXXVTI.  —  Starting  from  any  major  common  chord,  link 
together  three  common  chords,  all  having  one  sound  in  common. 
The  root,  3rd,  and  5th  of  the  antecedent  chord  should  be  taken  in 
succession  as  the  link-sound. 


STEP  CXXXVin. 
in  embellished  form. 


Present  the  progressions  of  Step  CXXXVI  I 


Note  79.  —  In  the  process  of  embellishment,  it  is  not  necessary  that 
the  link-sound  should  remain  throughout  in  one  individual  part.  It  is 
sufficient  that  the  student  realize  mentally  the  source  of  the  cohesion 
between  the  respective  harmonies.  The  chords  of  Ex.  117  are  here 
presented  in  varied  form  (Ex.  118). 


Chordal  Transference 


6i 


Ex.  1  18. 

Allegro. 

^-i- 

—  tfe-  ^ 

ifmi  J"      r~k 

J  —  «  —  £-t 

S 

-*  

\  VUJ4     B           •                                           I 

'  «_                  *                                                  —  « 

<            /^"                    ^  fr 

(W==  ^T-F?F^- 

-^r^f- 

t      bm  ,         m     r 

—  T—  1 

1^4  *  r 

Fed. 



*  b»   ' 
#  /v</. 

sHnH 

o       **Vf 

•  up                           -P 

•n 

Pp    ^  —  *-t-  F--tr+- 

ii 

-H4-^V  —  w* 

J  'IN  P>I  x= 

-     * 

S^Z  __^___i  p0  1  1_ 

^*-£bfe.   +- 

F           H>.  t-«.    •            ^^ 

RT  

1  1  1  1  — 

*  —  1   Kf  i   ^b«  *  P   1   1  [ 

H 

^n                   —  n  —  —  —  —  ^. 

^^  I         i  T      bJ. 

~~i  —  r~H 

II 

K? 

#  /v</. 

^<> 

* 

Note  80.  —  ^4  series  o/  /Aree  chords,  linked  together  in  the  manner 
iemonstrated,  may  be  brought  within  the  range  of  declared  tonality  by 

adding  a  perfect  cadence  suggested  a  by  the  progression  as  a  whole  or 
(b)  by  the  effect  of  the  third  chord.  The  entire  progression  of  Ex.  IIQ, 
for  instance,  prepares  the  mind  naturally  for  the  key  in  which  the  final 

Ex.  1  19. 


Ex.  1  19. 
Lento. 


!% 


s 


i 


I; 


-F— P- 


S 


E3^^ 


i 


^r~* 


±JL          ± 

iAa  rr  ^  IP 


• — p 


^ 


i 


cadence  is  cast.     In  Ex.  120,  on  the  contrary,  the  mind  waits  instinc- 
tively until  the  third  chord  determines  the  tonal  trend  of  the  passage. 


Ex.  12O. 
Vivace. 


62 


Harmony  in  Pianoforte-Study 


STEP  CXXXIX.  —  Starting  from  any  major  common  chord,  link 
together  three  common  chords,  all  having  one  sound  in  common. 
Add  a  perfect  cadence  in  accordance  with  the  tonal  suggestiveness  of 
each  passage.  In  Exs.  121  and  122  the  3rd  of  the  first  chord,  and 
in  Ex.  123  the  5th,  is  the  link-sound. 


Ex.  121. 


~^~- 


Ex.  122. 


-$*- 


Ex.  123. 


z. 

1                                         V  '-^ 

I/TV        _ 

\/£^ 

vjj       & 

£S                               lm.i^ 

\\                    K 

\j        & 
ka 

-&-        9" 
t»             U 

f~\' 

^G>           LT 

& 

~^f-  P-i9  

—  (>2?  UL^  — 

STEP  CXL.  —  Present  the  progressions  of  Step  CXXXIX  in  em- 
bellished form. 

Note  81.  —  Many  varieties  of  the  type  of  harmonic  movement  out- 
lined in  Note  79  may  be  discovered  by  the  enterprising  student.  The 
link-sound  —  to  name  but  one  example  —  may  be  placed  in  the  bass, 
entailing  thereby  the  use  of  chordal  inversions.  (Ex.  124.) 


Chordal  Transference 


Ex.  124. 

Largamente 


Note  82.  —  Chordal  transference  occurs  in  passing  from  one  key  to 
another,  a  harmonic  function  of  great  importance.  Thus,  any  one 
sound  of  a  common  chord  may  be  regarded,  prospectively,  as  root,  jrd, 
or  5th  of  a  common  chord,  major  or  minor;  or  as  root,  jrd,  5th,  or  Jth 
of 'the  chord  of  the  dominant  7th.  The  5th  of  the  chord  of  F  major  may, 
in  this  manner,  provide  a  means  of  transference  to  many  keys.  (Ex.  125 .) 


Ex.  125. 
A. 


B.     As  root. 


C.     As  minor  3rd. 


_g 


•& Tyyg — ;fg • 


D.     As  major  3rd. 


E.     As  5th. 


F.     As  root  of  dom.  7th. 


G.     As  3rd  of  dom.  7th.         H.     As  5th  of  dom.  7th.        I.     As  7th  of  dom.  7th. 


STEP  CXLI. —  Regard  the  root,  3rd  or  5th  of  any  major  common 
chord  as  providing  a  means  of  transition  to  other  chords,  forming  the 
several  progressions  upon  the  models  given  in  Ex.  125.  Complete 
each  progression  by  a  final  cadence  in  the  new  key.  The  examples 
should  be  played: — (a)  In  plain  chordal  form;  (6)  in  embellished 
form.  Ex.  126  is  an  embellishment  of  Ex.  125,  G. 


Harmony  in  Pianoforte-Study 


Ex.  126. 


STEP  CXLII.  —  Proceed  as  in  the  previous  Step,  taking,  in  each 
case,  a  different  minor  common  chord  as  the  antecedent  harmony. 


Note  83.  —  Chordal  transference  of  a  more  subtle  nature  may  take 
place  when  a  chord  is  conceived  as  possessing  a  dual  individuality; 
or,  in  other  words,  as  related  directly  to  two  keys,  to  the  antecedent  key  and 
to  a  new  key  remaining  to  be  established.  In  Ex.  127  the  third  or 
tonic  chord,  of  the  first  key  is  quitted  as  the  submediant  harmony  of  the 
new  key. 

Ex.  127. 


STEP  CXLin.  —  Establish  one  key  by  combining  not  less  than 
three  chords;  regard  the  last  chord  as  belonging  both  to  the  first 
and  to  another  key,  adding  two  or  three  chords  to  confirm  the  new 
tonality. 


Note  84.  —  Step  CXLIII  opens  up  a  mine  of  possibility  to  the 
student.  It  is  only  necessary  to  add  that  the  examples  should  also 
be  played  in  decorated  form.  Ex.  128  is  an  embellished  reproduction 
of  Ex.  127  and  is  illustrative  of  the  type  of  passage  now  to  be  attempted. 


Chordal  Transference 


Ex.  128. 

Grastioso. 


End  of  Part  IV. 


Sequences   and   Pedals 

Note  85.  —  Continuity  of  musical  thought  is  obtained  in  many 
ways;  in  some  cases,  by  the  use  of  devices  of  a  purely  decorative  origin. 
The  simple  harmonic  progression  at  A  in  Ex.  129  is  subsequently  re- 
peated on  successive  degrees  of  the  same  key,  and  a  complete  musical 
thought  is  the  result. 

Ex.  129. 


STEP  CXLIV.  —  Play  a  simple  harmonic  figure  of  two  chords 
Form  a  sequence  by  reproducing  this  figure  on  successive  degrees 
of  the  same  key  until  a  perfect  cadence  is  reached. 


Note  86.  —  No  limit  may  be  assigned  to  the  number  of  chords  con- 
tained within  the  model  progression,  save  only  that  which  is  necessarily 
imposed  by  an  accurate  perception  of  rhythmic  proportion.  In  Ex. 
jjo  the  model  contains  four  chords. 


Ex.  13O. 
Giocoso. 

"^••••j 

0        J        J 

H  *  ' 

m 

J_g  —     •      —  3_ 

/  ~^d^  —  '    —  ^  — 

•h  d 

—  4~.  i  -  — 

i  fn\jt 

™                ^ 

J                                         m                       m  '        * 

|  Vl/1-      £      •] 

•          *1 

d           ^i         r    "1                8— 

.  ^ 

^ 

^                L/                *" 

'  f^W       1* 

*~=j—               i 

£  F^  ^s  F—  a  

^:     P     **  

—  =1  — 

-•  •  —  =?  — 

U—        —  y  

66 


Sequences  and  Pedals 


i 


dim.    e    rail. 


^T 


^-•—fi    r    |    ,t  t  t  *    .f^fr  f    i 
*—  c=c^  ^  i  \j  -^T  r~^  ^  i  v  *j— -p—-—*1    ^  i 


£: 


^i 


i 


3f 


STEP  CXLV.  —  Form  models  consisting  of  more  than  two  chords 
and  proceed  as  in  Step  CXLIV. 


Note  87.  —  //  w  wo/  aw  essential  feature  of  the  sequence  that  the 
reproductions  of  the  model  should  occur  upon  the  consecutive  degrees 
of  the  scale.  Any  degrees  may  be  selected  by  the  player  to  form  the 
basis  of  the  thought  he  desires  to  express^  In  Ex.  131  one  degree  is 
missed  between  each  reproduction  of  the  model. 

Ex.  131. 

Andante, 


STEP  CXLVI.  —  Form  sequences  of  varied  extent,  omitting  re- 
productions upon  some  of  the  scale-degrees  of  each  key  chosen. 


Note  88.  —  The  sequences  treated  hitherto  occur  throughout  within 
the  key  of  the  model.  Progressions  of  this  nature  may,  however,  provide 
an  excellent  medium  for  modulation.  The  model  of  Ex.  132  is  trans- 
ferred through  keys  which  correspond  in  number  to  the  reproductions. 


68 


Harmony  in  Pianoforte-Study 


Ex.  132. 

Ben  marcato. 


pfa 


-&-_ 
_22 


m 


Note  89.  —  //  mW  &e  observed,  that  the  major  and  minor  modes  are 
used  interchangeably  in  the  above  sequence.  This  is  due  to  the  neces- 
sities which  underlie  the  employment  of  several  keys  in  close  succession. 
The  successful  formation  of  sequences  of  this  nature  demands  a  large 
amount  of  harmonic  experience  and  a  keen  sense  of  tonal  effect. 

STEP  CXLVII.  —  Having  formed  a  strongly  tonal  model,  repro- 
duce it  in  sequential  form  in  three  or  four  keys.  The  final  cadence 
may  be  in  the  original  key  or  in  that  of  the  last  reproduction. 


Note  90.  —  A  sound,  entirely  independent  of  the  harmony,  is  fre- 
quently sustained  throughout  a  series  of  chords.  A  sound  of  this  kind 
appears  in  instrumental  music  under  various  forms.  In  Ex.  Jjj  the 
pedal  —  or  pedal-point,  as  it  is  sometimes  called  —  is  observed  in  its 
simplest  form;  in  Ex.  134  it  is  decorated  by  octave  repetitions;  in 
Ex.  135  it  is  embellished  by  a  shake. 


Ex.  133 

So 

«0r0. 

l        1 

i 

JltfJ** 

^ 

J      fl 

1           1 

1 

i  <===»  i   1  1 

•  2 

-3  —  *  —  •—  • 

-J  —  4  —  J  —  f-i 

H  —  J  

—  J— 

J    J   1-1 

{(T)    v  tte 

Sr-J  

-i  —  *^*— 

-•!  9  •  ai— 

—  •  —  i 

—  5— 

1    ."I    H 

_ 

..     J      I       I       !      !     J       I      1 

*  3^3. 

J      -,-U, 

C^-J  —  ft'U  t!^.    ^  — 

s  — 

•  Jd  *  9= 

—  PJ  —  • 

—  •  — 

—  ~^  —  H 

b|>  u4 

—  jy  

xv  • 

-±- 

?y  —  ~M  M 

Sequences  and  Pedals 


Ex.  135. 
Con  brio. 


/K*f  —  i  

3  — 

q  ., 

t9>4— 

«T 
* 

**^ 

•£••            ^ 

n       h" 

«. 

u  *         •        ^ 

L/rt      J 

^        "JS 

p       1 

i            1        i        1        i  pv  • 

V  • 

M  i  r 

—f- 

1 

r-—J- 

J  J9- 

t  —  E—  F— 

^-M^1  ' 

=1 

J 

n^ 

F 

r\-         1 

i     n 

^^-«U  1 

^  

-5^  

^Ml 

/r. 


70  Harmony  in  Pianoforte-Study 

Note  91 .  —  The  scale-degrees  usually  employed  as  pedal-sounds  are 
the  tonic  and  dominant.  The  dominant  is  used  in  Ex.  133;  the  tonic 
in  Ex.  134;  while  in  Ex.  135  both  degrees  are  introduced. 

Note  92.  —  A  pedal  may  occur  above,  below,  or  actually  within  the 
accompanying  harmony.  Ex.  136  illustrates  the  employment  of  three 
inner  dominant  pedals  in  the  keys  of  F,  D  minor,  and  C,  respectively. 


Ex.  136. 
Vivo. 

*                 I>-                                                        *                 *                 * 

SCHUMANN.    Papillons. 

<g)R                    —  J  —  •  —  E: 

T  *  "Lr  r  r  r 

m        \)m           L                     • 

^f      ^»-  frip- 

Jt*        Li* 

r  f   f 

pv.o              r        r 

• 

C*       rs 

A              *                * 

i   r 

i    T  —  T— 

F-  —  F  —  •• 

STEP  CXLVm.  —  Form  harmonic  progressions  above,  below,  or 
around  the  tonic  or  dominant,  sustained  after  the  manner  illustrated 
by  Ex.  133  et  seq. 


End  of  Part  V. 


AUTHOR'S  NOTE 

In  the  remaining  Parts  of  this 
book,  it  will  be  taken  for  granted 
that  the  student  will  present 
each  progression  in  an  interest- 
ing and  musical  manner.  The 
directions  to  illustrate  the  ex- 
amples in  embellished  form 
will  therefore  appear  no  longer. 


PART  VI 

Chromatic   Harmony 


Note  93.  —  //  the  student  will  play  an  octave  of  a  major  scale  and, 
immediately  after,  sound  a  chord  foreign  to  the  key  (Ex.  IJ7),  this  chord 
will  in  all  probability  offend  his  tonal  sense.  The  use  of  chords  of  this 
nature  is,  however,  common  in  music  of  every  type,  and  it  is  important 
that  the  principles  under  which  they  are  introduced  should  be  experi- 

Ex.  137. 


mentally  grasped.  Two  points  call  for  special  apprehension:  —  (a) 
The  manner  of  the  introduction  of  such  chords,  or  their  retrospective 
aspect;  (b)  the  method  employed  in  preventing  disturbance  of  key. 

Note  94.  —  Chromatic  chords  are  often  introduced  by  applying  the 
principle  of  chordal  transference  described  in  Part  IV.  Thus,  the 
fourth  chord  of  Ex.  138  —  a  chord  which  appears  to  threaten  the  an- 
tecedent key  —  is  linked  to  the  previous  chord  by  the  one  sound  which 
they  possess  in  common. 

Ex.  138. 


STEP  CXLIX.  —  Establish  a  major  key  by  playing  not  less  than 
three  chords,  as  in  Ex.  138.  Follow  the  last  chord  by  another 
foreign  to  the  key,  but  which  possesses  a  sound  in  common  with  the 
previous  chord.  Each  example  will  accordingly  end  with  a  chro- 
matic chord  and  form  but  a  part  of  a  musical  thought. 
****** 

STEP  CL.  —  Transfer  Step   CXLIX  to  minor  keys.     Compare 
aurally  Ex.  139  with  Ex.  138. 

Ex.  139. 


7* 


Chromatic  Harmony 


73 


Note  95.  —  Chromatic  chords  may  also  be  introduced  by  a  mental 
recognition  of  their  tonal  environment  in  keys  other  than  those  in  which 
they  are  being  consciously  employed.  The  antecedent  key  of  Ex.  140 
is  F  major.  The  third  chord  may  be  mentally  referred  (i)  to  G  (Ex. 
141,  A),  (2)  to  E  minor  (Ex.  141,  B),  or  (3)  to  C^Ex.  141,  C).  Any 
chord  which  belongs  to  these  keys  may  therefore  be  introduced  with  good 
effect.  It  will  be  remarked  that,  in  harmonic  movement  of  this  nature, 
the  link-sound  is  often  absent;  further,  that  should  it  be  present,  it  is 
in  this  case  to  be  disregarded  as  a  means  of  cohesion. 


Ex.  14O. 


(1)          <.»)          (3^ 


STEP  CLI.  —  Establish  a  major  key  by  playing  not  less  than  three 
chords  in  that  key.  Refer  mentally  the  last  chord  to  another  key 
in  which  it  is  diatonic,  and  complete  the  passage  by  a  chord  belonging 
to  this  key  but  which  is  foreign  to  the  antecedent  key.  Each  ex- 
ample will  therefore  end  with  a  chromatic  chord  and  form  but  a 
part  of  a  musical  thought. 

N.B.  —  Many  examples  may  be  obtained  from  one  antecedent 
key. 


STEP  CLII.  —  Transfer  Step  CLI  to  minor  keys. 


Note  96.  —  Hitherto  the  chromatic  chord  has  been  dealt  with  retro- 
spectively; each  example  has  ended  with  the  unexpected  effect  of  a  har- 
mony which  has  seemed  to  annihilate  the  antecedent  key.  The  student 
is  now  required  to  work  in  the  contrary  direction.  He  is  asked  to  start 
from  a  chord  assumed  to  be  chromatic,  and,  by  the  harmonies  used  sub- 
sequently, to  prove  that  the  chromatic  chord  is  included  within  the  key 


74  Harmony  in  Pianoforte-Study 

of  the  whole  progression.  To  apprehend  the  point  involved,  the  fact 
should  be  recalled  that  the  fourth  chord  of  Ex.  138  (q.  v.)  tends  towards 
key-disturbance.  Consequently,  this  chord  requires  so  to  be  treated  that 
the  bias  towards  tonal  obscurity  becomes  corrected  in  the  process.  This 
is  effected  by  the  simple  expedient  of  following  the  chord  by  another  har- 
mony which  is  distinctly  characteristic  of  the  original  key,  and  which, 
in  particular,  corrects  the  disturbing  tendency  of  the  foreign  sound  —  F$. 
By  means  of  this  simple  stratagem,  the  tonality  of  Ex.  142  (which  should 
be  compared  with  Ex.  ij<5?)  remains  unimpaired  throughout. 


STEP  CLIII.  —  Having  played  one  octave  of  a  major  scale  to 
ensure  exact  tonal  perception,  the  student  will  sound  a  common 
chord  foreign  to  the  key ;  he  will  then  proceed  to  correct  the  possible 
key-disturbance  by  the  process  illustrated  in  Ex.  143.  It  is  much  to 
be  desired  that  each  example  should  close  with  a  tonic  cadence. 


Ex.  143. 

A.                                                                                      B. 

f\                                                                            /•" 

4  *  ^ 

Jf                                t  &      a>       & 

(*> 

—  =  H 

-«»  *?  *•  ^~ 

t>- 

Z 

ffi  FJi  — 

L«  —  H 

1 


Note  97.  —  //  must  be  specifically  understood  that  any  common  chord, 
major  or  minor,  may  be  introduced  into  any  key,  major  or  minor.  That 
some  chromatic  chords  are  difficult  to  treat  successfully  is  the  natural 
result  of  the  differences  between  close,  comparatively  close,  and  remote 
key-relationship.  A  wide  field  for  experiment  lies  here  for  the  re- 
sourceful student,  who  should  not  be  satisfied  until  he  is  able,  spon- 
taneously, to  employ  such  chords  with  entirely  musical  effect. 


STEP  CLIV.  —  Transfer  Step  CLIII  to  the  minor  mode. 

STEP  CLV.  —  Combine  the  processes  outlined  in  Steps  CXLIX 
and  CLIII.  Complete  harmonic  progressions  will  result,  in  each 
of  which  the  chromatic  chord  will  occupy  a  central  position.  Ex. 
142  may  be  regarded  as  a  simple  model. 


STEP  CLVI.  —  Transfer  Step  CLV  to  minor  keys.     (Ex.  144.) 


Chromatic  Harmony 


75 


Ex/  1 44. 

Graziosd, 


Note  98.  —  When  used  in  its  native  key,  the  chord  of  the  dominant 
7th  is  strictly  diatonic;  when  used  —  as  it  may  be  —  in  other  keys,  it 
becomes  chromatic.  The  successful  appropriation  of  this  chord  for 
use  in  other  keys  depends  to  some  extent  upon  the  comparative  nearness 
or  remoteness  of  the  tonal  relationship  of  those  keys  to  its  original  key. 
It  is,  for  example,  possible  to  introduce  the  dominant  jih  of  G  (Ex.  145} 
or  of  F  (Ex.  146}  into  the  key  of  C  with  but  little  difficulty,  since  both 
keys  are  related  tetrachordally  to  the  central  key;  but  the  problem  is  ac- 


Ex.  145. 


Ex.  146. 


centuated  in  proportion  as  the  scale-relationship  becomes  more  remote. 
In  Ex.  147,  for  instance,  the  dominant  fth  of  E  is  employed  as  a  chro- 
matic discord  in  the  key  of  C. 

Ex.  147. 


Note  99.  —  However  tonally  remote  may  be  a  chord  of  this  type,  it  is 
always  possible  to  recover,  as  it  were,  the  key  of  the  tonic  by  the  simple 
expedient  of  following  the  order  of  tetrachordal  alliance.  For  instance, 
Ex.  147  may  be  continued  as  in  Ex.  148  without  loss  as  regards  the 
antecedent  tonality;  but  a  progression  of  this  kind  is  avowedly  clumsy  and 
should  be  resorted  to  only  for  the  purpose  of  demonstration.  In  all 
cases,  it  should  be  the  aim  of  the  player  to  annul  as  soon  as  possible 


Harmony  in  Pianoforte-Study 


Ex.  148. 


the  disturbing  element  which  threatens  the  tonality;  and  this  can  usually 
be  effected  by  the  immediate  interposition  of  some  chord  specially  indica- 
tive of  the  original  key. 

STEP  CLVII.  —  Improvise  passages  in  various  major  keys,  in  the 
course  of  each  of  which  may  be  introduced  the  chord  of  the  domi- 
nant 7th  of  one  of  the  keys  allied  tetrachordally  with  the  key  se- 
lected. Follow  the  chromatic  chord  of  the  7th  by  the  dominant 
7th,  inverted  or  uninverted,  in  the  manner  illustrated  by  Exs.  145 
and  146. 


STEP  CLVHI.  —  Transfer  Step  CLVII  to  minor  keys. 


STEP  CLIX.  —  Proceed  as  in  Steps  CLVII  and  CLVIII,  but  in- 
troduce dominant  7ths  of  keys  more  remote  than  those  directly  con- 
nected tetrachordally  with  the  central  key.  A  few  examples  are 
appended. 


Ex.  149. 
Piacevole. 


Ex.  1  50. 

Deciso. 

-^. 

i!  r 

—  i  jn 

gy»Vj_f    r    r~i 
^KftVJ  x- 

=^=h 

3  J  —  « 

*= 

LJ  i 

Chromatic  Harmony 


77 


Ex.  151. 
Largo. 


*         *         *         *         * 


Note  loo.  —  A  chromatic  chord,  of  great  usefulness  to  the  player  may 
be  found  in  that  known  as  the  augmented  6th,  from  the  interval  between 
its  extreme  sounds.  It  is  generally  observed  in  three  distinct  forms:  — 
Ex.  152,  A,  accompanied  by  the  major  jrd,  its  simplest  form;  B,  by 
the  major  jrd  and  augmented  4th;  C,  by  the  major  jrd  and  perfect  $th. 


Ex.  152. 
A. 


C. 


iv    b»      I   b»      i— b-%        U 


Note  101.  —  The  chord  of  the  augmented  6th  is  usually  taken  upon 
the  minor  6th  and  minor  2nd  in  both  modes,  major  and  minor.  The  for- 
mer is  illustrated  by  Ex.  153,  the  latter  by  Ex.  154. 


Harmony  in  Pianoforte-Study 


Ex.  153. 

Ben  marcato. 


Ex.  154. 
Dolente. 


Note  102.  —  As  a  rule,  the  chord  of  the  augmented  6th  is  most  effec- 
tively resolved  when  the  sounds  which  constitute  the  interval  of  the  6th 
proceed  in  contrary  motion,  or  progress  a  semitone  upwards  or  down- 
wards, or  when  one  remains  to  be  a  sound  of  the  following  harmony. 
The  chord  is,  however,  susceptible  of  great  variety  in  respect  to  harmonic 
resolution.  The  following  are  examples: 


B. 


Ex.  1 

A. 

55. 

Lf   f\ 

vf  ^3     ^^ 

—  , 

•V  |\  (  \       ^~ 

it      1 

^•^ 

T'ir  ^5           tf~ 

oBxEk2 

H^/ 

.    -f 

-s>- 

a'£    (- 

t/C' 

^  f2  — 

-^  o 

H  — 

f\     £l        £*•              £S. 

<5>              1 

ifno 

^      I  ij      | 

1^1              r*f[ 

\!^L>^s 

U  ^3            22 

S         1 

r^v  •  t"i 

?£ 

^^            /*^) 

I'M 

J[ 

C. 


D. 


-2- 


Jjljj 

-<S — fctt-U)   -U<S <§ 


3<» B>- 


1 


^% 


nr^^ 


STEP  CLX.  —  Having  established  a  major  key,  introduce  the  chord 
of  the  augmented  6th  on  the  minor  6th,  and  complete  the  progres- 
sion by  further  harmonies  in  the  original  key.  The  chord  should 
be  exemplified  in  the  three  forms.  (Ex.  156.) 


Chromatic  Harmony 


79 


Ex.  156. 

Pastorale. 


f^-f— M- 


Jz*. 


STEP  CLXI.  —  Transfer  Step  CLX  to  minor  keys.     Begin  by 
playing  Ex.  156  in  the  tonic  minor. 


STEP  CLXII.  —  Proceed  as  in  Step  CLX,  introducing  the  aug- 
mented 6th  on  the  minor  2nd  of  the  key.  The  chord  should  be 
exemplified  in  the  three  forms.  (Ex.  157.) 


Ex.  157. 

Alia  tnarcia  funebre. 


frT-4-       i         i 

-T— r^    J    S 

*:    i    i     i     J: 


"-IT- 
sonoro. 


^' 


nTT  -^' 


g^j  ^ 

^filS        »» 


—fS1 ' <S 


<a 


£ 


II 


STEP  CLXTII.  —  Transfer  Step  CLXII  to  minor  keys.     Begin  by 
playing  Ex.  157  in  the  tonic  minor. 

End  of  Part  VI. 


PART  VII 
The   Building  of  the   Dominant  Discord 

Note  103.  —  The  discord  of  the  dominant  is  the  controlling  element 
in  all  harmonic  expression.  The  most  elementary  form  of  the  chord  — 
as  a  discord  —  is  that  known  as  the  dominant  7th,  which  consists 
merely  of  a  7th  added  to  the  common  chord  of  the  dominant.  It  will  be 
remarked  that  this  chord  is  built  of  thirds  placed  each  above  the  other, 
and  the  fact  affords  a  clue  to  its  enlargement,  this  being  effected  by 
adding  further  thirds  to  the  fundamental  chord.  The  added  sounds 
vary  in  pitch  according  to  the  respective  modes.  Ex.  158,  A,  illus- 
trates the  complete  dominant  discord  in  the  major  key;  B,  the  same  in 
the  minor. 

Ex.  158. 

/->  •>    -•-        -9- 

r\ *___^__ 

~M 


a  

i               Ylm      <**      ~                    Ifti'fft           II 
u       h«    ^                                            1     W?           M 

,  «  P»   P*  |-?i 

*       rteb~  -T^~ 

-f— 

8               46               8               7           -^- 

•&- 


STEP  CLXIV.  —  Build  up  the  entire  dominant  discord  (a)  in  vari- 
ous major  keys;   (b)  in  various  minor  keys. 


Note  104.  —  //  is  manifest  that  the  chords  built  up  in  Step  CLXIV 
are  so  extensive  as  to  be  unmanageable  for  ordinary  use;  they  are,  in 
fact,  heard  but  seldom  in  complete  form.  As  a  rule,  the  dominant 
discord  is  most  effective  when  it  occurs  in  parts  or  sections.  The 
following  illustrate  some  of  the  many  possible  combinations.  The 
figures  correspond  with  the  numbered  members  of  the  chord  in  Ex.  158. 


Ex.  159. 
A. 

B. 

|, 

c. 

1             J 

J               1 

1      If.    A 

IK^jl 

1  a^y 

J             J 

/f-u4-  .    ! 

£j    h-i 

m       o. 

•            • 

(foPj.  7&b  J_ 

_JZd_J2*  g 

€          &      IA 

1-&- 

*    J 

&&_• 

—  0  \-£4.  l-Op!  

lr-4- 


80 


The  Building  of  the  Dominant  Discord 


81 


J 


I 


«-^.'  J. 


-49- 


£ 

-6S>- 


r 


r 


Note  105.  —  A  great  difference  exists  between  the  four  lowest  mem- 
bers of  the  dominant  discord  (or  those  which  form  the  chord  of  the  domi- 
nant 7th)  and  the  three  added  sounds.  The  latter  often  partake  of  the 
nature  of  accented  auxiliary  sounds  and  are  then  followed  immediately 
by  the  concordant  sounds  one  degree  above  or  below,  while  the  rest  of  the 
chord  remains.  In  Ex.  160,  A ,  the  first  added  sound  (otherwise  called 
the  pth)  falls  to  the  octave,  the  rest  of  the  chord  remaining  for  subsequent 
resolution;  in  B  and  C,  the  second  added  sound  (otherwise  known  as 
the  nth)  and  the  third  added  sound  (or  ijth)  are  similarly  treated. 

Ex.  16O. 


B. 

^  N         1 

U  i  f 

B 

•         i*  ' 

/Lbr 

J 

c* 

Im  C 

• 

.  «*  • 

ik\)  r 

1 

~T         ^~ 

£)f-£ 

-fc  1 

3E 

33 


i 


j=i 


i 


r 

STEP  CLXV.  —  Combine  the  root,  3rd,  7th  and  9th  of  the  domi- 
nant discord  in  various  major  keys.  Resolve  the  9th  upon  the  8th, 
and  complete  the  progression  by  a  perfect  cadence  in  the  tonic. 
(Ex.  161.) 

Ex.  161. 
Deciso. 

tf+ 


f:i|;i  i 


i 


m 


frsemfre 


P 


E* 


wvm 

I 


^e 


-POL 


Harmony  in  Pianoforte-Study 


STEP  CLXVL—  Transfer  Step  CLXV  to  minor  keys.  Begin  by 
playing  Ex.  161  in  the  tonic  minor  and  with  the  minor  9th. 

STEP  CLXVII. —  Combine  the  root,  5th,  yth  and  nth  of  the 
dominant  discord  in  various  keys,  major  and  minor.  Resolve  the 
nth  upon  the  3rd,  and  complete  each  progression  by  a  perfect  ca- 
dence in  the  tonic.  (Ex.  162.) 

Ex.  162. 

Piangevole. 


STEP  CLXVIII.  —  Combine  the  root,  3rd,  7th  and  I3th  of  the 
dominant  discord  in  various  major  keys.  Resolve  the  I3th  upon  the 
5th,  and  complete  each  progression  by  a  perfect  cadence  in  the  tonic. 
(Ex.  163.) 


Ex.  163. 

Andantino. 


ii 


J: 


m 


$ 


•— *- 


F* 


m 

-9 


STEP  CLXIX.  —  Transfer  Step  CLXVIII  to  minor  keys.  Begin 
by  playing  Ex.  163  in  the  tonic  minor,  substituting  the  minor  I3th. 

****** 

Note  106.  —  Although  the  major  Qth  and  jj th  and  the  minor  gfh  and 
ijth  belong  naturally  to  the  major  and  minor  modes  respectively,  they 
are  nevertheless  used  interchangeably  in  either. 

STEP  CLXX.  —  Repeat  the  combinations  of  Steps  CLXV  and 
CLXVIII,  proceeding  to  the  minor  in  the  final  cadence. 

Note  107.  —  The  varied  resolutions  of  the  chord  of  the  dominant  7th 
exemplified  in  Note  47  are  obviously  applicable  to  the  dominant  discord 
considered  as  a  whole,  and  this  fact  should  stimulate  the  student  in  the 
direction  of  fruitful  investigation  and  experiment. 

End  of  Part  VH. 


PART    VIII 

The   Enharmonic   Principle 

Note  1 08.  —  The  enharmonic  principle  permeates  every  form  of 
musical  expression.  Its  most  objective  phase  is  that  concerned  with 
change  of  key.  Modulation,  for  example,  may  be  easily  effected  by 
prolonging  one  sound  of  a  chord  and  at  the  same  time  referring  it  men- 
tally to  a  key  indicated  by  one  of  its  enharmonic  counterparts.  (Ex. 
164.) 


Ex.  164- 
Animate. 

,  n 

i     r 

r                   v 

J                       J       M- 

H£  ^-W-H»W  Jj   .        --{?,    -'^Mg^« 

-^                'ftf               f 

••-  h 


^Si 


X    X 


STEP  CLXXI.  —  Having  established  a  major  or  a  minor  key,  re- 
peat one  of  the  sounds  of  the  last  chord  after  the  manner  of  Ex.  164; 
then,  by  enharmonic  change,  proceed  to  the  new  key. 


Note  109.  —  The  enharmonic  transition  of  Ex.  164  is  effected  by 
the  simplest  of  means:  by  the  mere  mental  reference  of  a  sound  to  an- 
other tonic.  The  principle,  however,  is  illustrated  in  a  fuller  measure 
by  its  adaptation  to  a  complete  chord.  The  most  striking  of  the  chords 

83 


Harmony  in  Pianoforte-Study 


adapted  specially  to  enharmonic  treatment  is  that  known  as  the  chord 
of  the  diminished  7th,  a  chord  formed  by  the  3rd,  4th,  7th  and  minor 
gth  of  the  dominant  discord.  (Ex.  165.}  The  versatility  of  this  chord 
is  unequalled  by  any  other  harmonic  combination.  The  chord  given 


Ex.  165. 


in  Ex.  165  is  shown  in  Ex.  166  as  providing  a  means  of  passing  into 
all  the  twelve  keys,  major  and  minor;  from  which  it  will  appear  that 
the  player  has  but  to  adjust  the  dominant  chord  of  the  new  key  to  the 
part-distribution  of  the  chord  of  the  diminished  7th  to  effect  at  once  the 
desired  modulation. 


Ex.  166. 


G. 


H. 


?- 

kg    I 
L  i 


a      - 


e 


J. 


K. 


The  Enharmonic  Principle  85 

STEP  CLXXII.  —  Play  the  twelve  chords  of  the  diminished  7th 
in  unbroken  succession.  Harmonize  the  chromatic  scale  by  a 
series  of  the  same  chords. 

Note  no.  —  Certain  composers  of  pianoforte  music  have  particu- 
larly favoured  the  form  of  progression  directed  in  Step  CLXXII, 
(Ex.  167.} 


Ex.  167. 


CHOPIN.    Study,  Op.  25,  No.  6. 


STEP  CLXXni.  —  Pass  into  each  of  the  twelve  keys,  major  and 
minor,  from  any  one  of  the  twelve  chords  of  the  diminished  7th. 
In  each  case,  contrive  the  modulation  by  playing  the  dominant 
harmony  of  the  new  key  immediately  after  the  chord  of  the  di- 
minished yth.  (Ex.  1 68.) 


Ex.  168. 

Tranquillo. 


^  I  A- 


Jt?l 


86 


Harmony  in  Pianoforte-Study 


Note  in.  —  It  will  not  have  escaped  the  notice  of  the  observant  stu- 
dent that  the  chords  of  the  dominant  7th  and  the  augmented  6th,  accom- 
panied by  the  3rd  and  5th,  are  represented  by  the  same  keys  upon  the 
pianoforte.  This  is  but  another  instance  of  the  working  of  the  enhar- 
monic principle;  yet  nothing  can  be  more  different  in  effect  than  the 
two  chords  in  their  respective  tonal  environments.  Cf.  the  chords  marked 
by  the  asterisk  in  Exs.  169  and  170. 

Ex.  169. 


c^ 


Ex.  1 

4       Ott 

7 

O. 

* 

VffQ 

/L     '» 

1 

f(T\     /i 

f 

J 

\J    *t 

^ 

• 

'6 

* 

"t                  "' 
*         *        -t 

r 

^j 

• 

^J   *t? 

^ 

-P  0  « 

STEP  CLXXIV.  —  Contrive  examples  of  modulation  through  the 
medium  of  the  dominant  yth  changed  enharmonically  into  the  chord 
of  the  augmented  6th;  or  vice  versa,  by  the  enharmonic  change  of 
the  augmented  6th  to  the  dominant  yth. 


Note  112.  —  Like  all  other  chords,  that  of  the  augmented  6th  is 
susceptible  of  inversion,  and  the  student  will  do  well  to  discover  the 
several  inversions  for  himself,  making  use  of  each  in  the  course  of 
modulatory  and  non-modulatory  progressions. 

End  of  Part  VIH. 


THE  AUTHOR'S  FINAL  NOTE 

It  is  to  be  hoped  that  the  student  who  has  diligently  pursued  his 
way  through  the  foregoing  pages  will  have  discovered  himself  pos- 
sessed of  a  new  power  —  that  of  musical  self-expression  founded  upon 
knowledge.  The  act  of  extemporization  —  as  it  is  called  —  is  not 
to  be  regarded  as  an  exotic  in  respect  to  musical  study;  as  something 
which  comes  to  the  musician,  as  it  were,  by  stealth;  as  merely  a 
desirable  but  inessential  section  of  musicianship.  On  the  contrary, 
the  power  to  extemporize,  to  give  musical  expression  to  thought  and 
mood,  should  be  held  to  be  the  aim  of  the  student  as  well  as  the  joy 
of  the  cultivated  artist.  Although  it  is  true  that  not  a  few  lovers  of 
music  are  able  with  more  or  less  success  to  give  spontaneous  expres- 
sion to  their  personal  thoughts,  yet  it  should  ever  be  remembered 
that  every  power  called  into  activity  by  the  workings  of  the  art- 
instinct  is  not  only  intended  to  be  cultivated,  but  is,  moreover, 
infinitely  worth  the  cultivating.  However  apparently  skilful  the  art 
of  the  extemporaneous  player,  there  can  be  for  him  no  real  progress 
unless  the  power  he  displays  be  the  offspring  of  fundamental  knowl- 
edge; and,  to  such  a  player,  one  of  the  most  essential  of  all  forms  of 
musical  knowledge  is  that  comprehended  by  the  term  harmony.  It 
is  the  harmonic  substratum  which  provides  a  lodgment  for  his  fleet- 
ing thoughts;  it  is  the  harmonic  chain  which  helps  to  bind  them  in 
a  close  unity;  it  is  the  harmonic  divisions  which  point  the  way  to  a 
true  rhythmic  alignment,  the  harmonic  colouring  which  reflects  mood 
and  contributes  its  wealth  of  effect  to  the  portrayal  of  climax  and 
repose.  In  no  respect,  indeed,  is  it  possible  to  underrate  the  im- 
portance of  a  clear  grasp  of  the  harmonic  principles  of  music.  And 
if  it  should  come  to  pass  that  those  readers  who  have  hitherto  floun- 
dered hopelessly  in  their  struggles  to  attain  the  power  of  instrumental 
self-expression  become  conscious  of  receiving  help  and  inspiration 
from  the  teaching  of  these  pages,  this  little  book  will  have  abun- 
dantly achieved  the  purpose  for  which  it  was  written. 


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